Academic literature on the topic 'Electrical engineering-time series analysis'

The framework of the theory of nonlinear dynamics provides powerful concepts and algorithms to study complicated dynamics such as brain electrical activity (electroencephalogram, EEG). Although different influencing factors render the use of nonlinear measures in a strict sense problematic, converging evidence from various investigations now indicates that nonlinear EEG analysis provides a means to reliably characterize different states of physiological and pathophysiological brain function. We here focus on applications of nonlinear EEG analysis in epileptology. Epilepsy affects more than 50 million individuals worldwide – approximately 1% of the world's population. The disease is characterized by a recurrent and sudden malfunction of the brain that is termed seizure. Nonlinear EEG analysis techniques allow to reliably identify the seizure generating structure (epileptic focus) in different areas of the brain even during seizure-free intervals, to disentangle complex spatio-temporal interactions between the epileptic focus and other areas of the brain, and to define a specific state predictive of an impending seizure. Nonlinear EEG analysis provides supplementary information about the epileptogenic process in humans, contributes to an improvement of the presurgical evaluation of epilepsy patients, and offers a basis for the development of new therapy concepts for seizure prevention.

When the TCSC steady-state operation, the thyristor turn-on and turn-off time is definite, the changing for TCSC electric capacity voltage and thyristor electric current is with the periodicity and symmetry.Thyristor controlled series compensation technology is fixed series compensation technology foundation, which is meet the needs for adaptation electrical power system operation control developing. With changes the triggering angle for thyristor suitably, then can realize the TCSC equivalent reactance fast, continuously and adjusts smoothly, provides the controllable series compensation for the system, as to achieve increases the system transmitting capacity, enhance the transition condition stability, the damping power oscillation, and the purpose for improvement system tidal current distribution. Although in the entire time axis, obtains the analytic expression for TCSC running status variable is difficulty, but as long as had determined the analytic expression for various electrical quantity in a power frequency cycle, according to the stable state movement's symmetry and periodicity, we can determine the steady state profile that in the entire time axis, and then analyses the TCSC electric circuit’s steady-state characteristic with the time domain computation method. In this paper, topological analysis for TCSC operation established by formula, and then carries on the time domain partition to the TCSC electric circuit solution, finally obtains the steady state fundamental frequency impedance model for TCSC. This paper steady-state characteristic analysis is mainly carries on the topological analysis method to the TCSC main circuit, then establishes the stable state base frequency impedance model for TCSC, and analyses the resonance question for TCSC simultaneously. Then studies TCSC the steady- state characteristic, and with modeling and simulation on them to do further research and analysis, and utilizes the solution method for transformation territory, namely applies the Laplace transform solution equation of state. Thus can be obtained the zero-input response and zero status response formula for system.

Relevance of research. In order to reduce energy losses, an accurate and timely forecast of the amount of consumed electricity is necessary. Accurate forecasting of electrical loads of industrial enterprises and their divisions (productions, workshops, departments etc.) allows planning of normal operating conditions, concluding contracts for the electricity supply with the electricity supply company under more favorable conditions, and improving the electricity quality, which ultimately affects the final cost of the products produced by an enterprise. So far, more than 150 forecasting methods of electrical loads have been developed. Usually, the most convenient one is selected based on the forecaster experience by creating and analyzing several forecasting models in order to identify the best. Therefore, in order to simplify the forecasting procedure, it is necessary to develop the methodology for forecasting analysis. This methodology should enable canceling forecasting algorithms that will create lower quality forecasts. The main objective is to develop the methodology for making a forecasting analysis of power consumption on the example of a pumping station of an enterprise with a continuous cycle of work to increase the efficiency of energy consumption and implementation of energy-saving measures. Objects of research: the process of forecasting electrical loads of a pumping station of the enterprise with a continuous cycle of work. Methods of research: fundamental principles of the theory of electrical engineering, statistical methods for power consumption forecasting, the method for detecting the trend of radio signals, and fractal analysis of time series. Research results. The methodology for forecasting analysis of power consumption, which makes it possible to apply the most appropriate methods to forecast the operational power consumption, is developed. For the first time, the radio signal trend detection method is applied to identify the trend of electrical loads. The variation ranges of the fractal parameters of time series of electrical loads are established depending on the variation coefficient of the time series for different periods of time. The Brown method of exponential smoothing that is used to forecast the electrical loads, in the case of identifying the smoothing constant α is in the beyond set ( ), is further improved. The regularity of changes in the fractal parameters of time series of power consumption of a pumping station with an increase in the time series duration and their field of application are explained.

Relevance of research. In order to reduce energy losses, an accurate and timely forecast of the amount of consumed electricity is necessary. Accurate forecasting of electrical loads of industrial enterprises and their divisions (productions, workshops, departments etc.) allows planning of normal operating conditions, concluding contracts for the electricity supply with the electricity supply company under more favorable conditions, and improving the electricity quality, which ultimately affects the final cost of the products produced by an enterprise. So far, more than 150 forecasting methods of electrical loads have been developed. Usually, the most convenient one is selected based on the forecaster experience by creating and analyzing several forecasting models in order to identify the best. Therefore, in order to simplify the forecasting procedure, it is necessary to develop the methodology for forecasting analysis. This methodology should enable canceling forecasting algorithms that will create lower quality forecasts. The main objective is to develop the methodology for making a forecasting analysis of power consumption on the example of a pumping station of an enterprise with a continuous cycle of work to increase the efficiency of energy consumption and implementation of energy-saving measures. Objects of research: the process of forecasting electrical loads of a pumping station of the enterprise with a continuous cycle of work. Methods of research: fundamental principles of the theory of electrical engineering, statistical methods for power consumption forecasting, the method for detecting the trend of radio signals, and fractal analysis of time series. Research results. The methodology for forecasting analysis of power consumption, which makes it possible to apply the most appropriate methods to forecast the operational power consumption, is developed. For the first time, the radio signal trend detection method is applied to identify the trend of electrical loads. The variation ranges of the fractal parameters of time series of electrical loads are established depending on the variation coefficient of the time series for different periods of time. The Brown method of exponential smoothing that is used to forecast the electrical loads, in the case of identifying the smoothing constant α is in the beyond set ( ), is further improved. The regularity of changes in the fractal parameters of time series of power consumption of a pumping station with an increase in the time series duration and their field of application are explained.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.
Includes bibliographical references (p. 153-159).
by James M. Hutchinson.
Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 153-157).
We introduce a Bayesian discrete-time framework for switching-interaction analysis under uncertainty, in which latent interactions, switching pattern and signal states and dynamics are inferred from noisy and possibly missing observations of these signals. We propose reasoning over posterior distribution of these latent variables as a means of combating and characterizing uncertainty. This approach also allows for answering a variety of questions probabilistically, which is suitable for exploratory pattern discovery and post-analysis by human experts. This framework is based on a Bayesian learning of the structure of a switching dynamic Bayesian network (DBN) and utilizes a states-pace approach to allow for noisy observations and missing data. It generalizes the autoregressive switching interaction model of Siracusa et al. [50], which does not allow observation noise, and the switching linear dynamic system model of Fox et al. [16], which does not infer interactions among signals. We develop a Gibbs sampling inference procedure, which is particularly efficient in the case of linear Gaussian dynamics and observation models. We use a modular prior over structures and a bound on the number of parent sets per signal to reduce the number of structures to consider from super-exponential to polynomial. We provide a procedure for setting the parameters of the prior and initializing latent variables that leads to a successful application of the inference algorithm in practice, and leaves only few general parameters to be set by the user. A detailed analysis of the computational and memory complexity of each step of the algorithm is also provided. We demonstrate the utility of our framework on different types of data. Different benefits of the proposed approach are illustrated using synthetic data. Most real data do not contain annotation of interactions. To demonstrate the ability of the algorithm to infer interactions and the switching pattern from time-series data in a realistic setting, joystick data is created, which is a controlled, human-generated data that implies ground truth annotations by design. Climate data is a real data used to illustrate the variety of applications and types of analyses enabled by the developed methodology. Finally, we apply the developed model to the problem of structural health monitoring in civil engineering. Time-series data from accelerometers located at multiple positions on a building are obtained for two laboratory model structures and a real building. We analyze the results of interaction analysis and how the inferred dependencies among sensor signals relate to the physical structure and properties of the building, as well as the environment and excitation conditions. We develop time-series classification and single-class classification extensions of the model and apply them to the problem of damage detection. We show that the method distinguishes time-series obtained under different conditions with high accuracy, in both supervised and single-class classification setups.
by Zoran Dzunic.
Ph. D.

In this report six different models for predicting the electrical spot price on the Nordic power exchange, Nord Pool, are developed and compared. They are evaluated against the already existing model as well as the naive test, which is a forecast where the last week’s observations are used as a prognosis for the coming week. The models developed are constructed so that the models for different time resolutions are combined to create a full model. Harmonic regression with a linear trend are used to identify a yearly trend while SARIMAX/SARIMA time series models are used on a daily and hourly basis to reveal dependencies in the data.   The model with the best prediction performance is shown to be a SARIMAX model with temperature as exogenous variable on a daily resolution, together with a SARIMA model on an hourly resolution. With an average MAPE of 12.69% and a MAPE2 of 6.90% it has the smallest prediction error out of all of the competing models when doing one week forecasts on the whole year 2009.

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.
Includes bibliographical references (leaves 133-150).
This thesis describes the current state-of-the-art in nonlinear time series analysis, bringing together approaches from a broad range of disciplines including the non-linear dynamical systems, nonlinear modeling theory, time-series hypothesis testing, information theory, and self-similarity. We stress mathematical and qualitative relationships between key algorithms in the respective disciplines in addition to describing new robust approaches to solving classically intractable problems. Part I presents a comprehensive review of various classical approaches to time series analysis from both deterministic and stochastic points of view. We focus on using these classical methods for quantification of complexity in addition to proposing a unified approach to complexity quantification encapsulating several previous approaches. Part II presents robust modern tools for time series analysis including surrogate data and Volterra-Wiener modeling. We describe new algorithms converging the two approaches that provide both a sensitive test for nonlinear dynamics and a noise-robust metric for chaos intensity.
by Akhil Shashidhar.
M.Eng.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 183-190).
In this dissertation we investigate the problem of reasoning over evolving structures which describe the dependence among multiple, possibly vector-valued, time-series. Such problems arise naturally in variety of settings. Consider the problem of object interaction analysis. Given tracks of multiple moving objects one may wish to describe if and how these objects are interacting over time. Alternatively, consider a scenario in which one observes multiple video streams representing participants in a conversation. Given a single audio stream, one may wish to determine with which video stream the audio stream is associated as a means of indicating who is speaking at any point in time. Both of these problems can be cast as inference over dependence structures. In the absence of training data, such reasoning is challenging for several reasons. If one is solely interested in the structure of dependence as described by a graphical model, there is the question of how to account for unknown parameters. Additionally, the set of possible structures is generally super-exponential in the number of time series. Furthermore, if one wishes to reason about structure which varies over time, the number of structural sequences grows exponentially with the length of time being analyzed. We present tractable methods for reasoning in such scenarios. We consider two approaches for reasoning over structure while treating the unknown parameters as nuisance variables. First, we develop a generalized likelihood approach in which point estimates of parameters are used in place of the unknown quantities. We explore this approach in scenarios in which one considers a small enumerated set of specified structures.
(cont.) Second, we develop a Bayesian approach and present a conjugate prior on the parameters and structure of a model describing the dependence among time-series. This allows for Bayesian reasoning over structure while integrating over parameters. The modular nature of the prior we define allows one to reason over a super-exponential number of structures in exponential-time in general. Furthermore, by imposing simple local or global structural constraints we show that one can reduce the exponential-time complexity to polynomial-time complexity while still reasoning over a super-exponential number of candidate structures. We cast the problem of reasoning over temporally evolving structures as inference over a latent state sequence which indexes structure over time in a dynamic Bayesian network. This model allows one to utilize standard algorithms such as Expectation Maximization, Viterbi decoding, forward-backward messaging and Gibbs sampling in order to efficiently reasoning over an exponential number of structural sequences. We demonstrate the utility of our methodology on two tasks: audio-visual association and moving object interaction analysis. We achieve state-of-the-art performance on a standard audio-visual dataset and show how our model allows one to tractably make exact probabilistic statements about interactions among multiple moving objects.
by Michael Richard Siracusa.
Ph.D.

An analysis of the experience of professional training bachelors of electromechanics in Ukraine and abroad made it possible to determine that one of the leading trends in its modernization is the synergistic integration of various engineering branches (mechanical, electrical, electronic engineering and automation) in mechatronics for the purpose of design, manufacture, operation and maintenance electromechanical equipment. Teaching mechatronics provides for the meaningful integration of various disciplines of professional and practical training bachelors of electromechanics based on the concept of modeling and technological integration of various organizational forms and teaching methods based on the concept of mobility. Within this approach, the leading learning tools of bachelors of electromechanics are mobile Internet devices (MID) – a multimedia mobile devices that provide wireless access to information and communication Internet services for collecting, organizing, storing, processing, transmitting, presenting all kinds of messages and data. The authors reveals the main possibilities of using MID in learning to ensure equal access to education, personalized learning, instant feedback and evaluating learning outcomes, mobile learning, productive use of time spent in classrooms, creating mobile learning communities, support situated learning, development of continuous seamless learning, ensuring the gap between formal and informal learning, minimize educational disruption in conflict and disaster areas, assist learners with disabilities, improve the quality of the communication and the management of institution, and maximize the cost-efficiency. Bachelor of electromechanics competency in modeling of technical objects is a personal and vocational ability, which includes a system of knowledge, skills, experience in learning and research activities on modeling mechatronic systems and a positive value attitude towards it; bachelor of electromechanics should be ready and able to use methods and software/hardware modeling tools for processes analyzes, systems synthesis, evaluating their reliability and effectiveness for solving practical problems in professional field. The competency structure of the bachelor of electromechanics in the modeling of technical objects is reflected in three groups of competencies: general scientific, general professional and specialized professional. The implementation of the technique of using MID in learning bachelors of electromechanics in modeling of technical objects is the appropriate methodic of using, the component of which is partial methods for using MID in the formation of the general scientific component of the bachelor of electromechanics competency in modeling of technical objects, are disclosed by example academic disciplines “Higher mathematics”, “Computers and programming”, “Engineering mechanics”, “Electrical machines”. The leading tools of formation of the general scientific component of bachelor in electromechanics competency in modeling of technical objects are augmented reality mobile tools (to visualize the objects’ structure and modeling results), mobile computer mathematical systems (universal tools used at all stages of modeling learning), cloud based spreadsheets (as modeling tools) and text editors (to make the program description of model), mobile computer-aided design systems (to create and view the physical properties of models of technical objects) and mobile communication tools (to organize a joint activity in modeling).

The whitefly (Bemisia tabaci) is a serious agricultural pest that afflicts a wide variety of ornamental and vegetable crop species. To enable survival on a great diversity of host plants, whiteflies must have the ability to avoid or detoxify numerous different plant defensive chemicals. Such toxins include a group of insect-deterrent molecules called glucosinolates (GSs), which also provide the pungent taste of Brassica vegetables such as radish and cabbage. In our BARD grant, we used the whitefly B. tabaci and Arabidopsis (a Brassica plant model) defense mutants and transgenic lines, to gain comprehensive understanding both on plant defense pathways against whiteflies and whitefly defense strategies against plants. Our major focus was on GSs. We produced transgenic Arabidopsis plants accumulating high levels of GSs. At the first step, we examined how exposure to high levels of GSs affects decision making and performance of whiteflies when provided plants with normal levels or high levels of GSs. Our major conclusions can be divided into three: (I) exposure to plants accumulating high levels of GSs, negatively affected the performance of both whitefly adult females and immature; (II) whitefly adult females are likely to be capable of sensing different levels of GSs in their host plants and are able to choose, for oviposition, the host plant on which their offspring survive and develop better (preference-performance relationship); (III) the dual presence of plants with normal levels and high levels of GSs, confused whitefly adult females, and led to difficulties in making a choice between the different host plants. These findings have an applicative perspective. Whiteflies are known as a serious pest of Brassica cropping systems. If the differences found here on adjacent small plants translate to field situations, intercropping with closely-related Brassica cultivars could negatively influence whitefly population build-up. At the second step, we characterized the defensive mechanisms whiteflies use to detoxify GSs and other plant toxins. We identified five detoxification genes, which can be considered as putative "key" general induced detoxifiers because their expression-levels responded to several unrelated plant toxic compounds. This knowledge is currently used (using new funding) to develop a new technology that will allow the production of pestresistant crops capable of protecting themselves from whiteflies by silencing insect detoxification genes without which successful host utilization can not occur. Finally, we made an effort to identify defense genes that deter whitefly performance, by infesting with whiteflies, wild-type and defense mutated Arabidopsis plants. The infested plants were used to construct deep-sequencing expression libraries. The 30- 50 million sequence reads per library, provide an unbiased and quantitative assessment of gene expression and contain sequences from both Arabidopsis and whiteflies. Therefore, the libraries give us sequence data that can be mined for both the plant and insect gene expression responses. An intensive analysis of these datasets is underway. We also conducted electrical penetration graph (EPG) recordings of whiteflies feeding on Arabidopsis wild-type and defense mutant plants in order to determine the time-point and feeding behavior in which plant-defense genes are expressed. We are in the process of analyzing the recordings and calculating 125 feeding behavior parameters for each whitefly. From the analyses conducted so far we conclude that the Arabidopsis defense mutants do not affect adult feeding behavior in the same manner that they affect immatures development. Analysis of the immatures feeding behavior is not yet completed, but if it shows the same disconnect between feeding behavior data and developmental rate data, we would conclude that the differences in the defense mutants are due to a qualitative effect based on the chemical constituency of the phloem sap.

This report is one of a series of reports documenting the methods and findings of a multi-year, multi-disciplinary project coordinated by the Pacific Earthquake Engineering Research Center (PEER) and funded by the California Earthquake Authority (CEA). The overall project is titled “Quantifying the Performance of Retrofit of Cripple Walls and Sill Anchorage in Single-Family Wood-Frame Buildings,” henceforth referred to as the “PEER–CEA Project.” The overall objective of the PEER–CEA Project is to provide scientifically based information (e.g., testing, analysis, and resulting loss models) that measure and assess the effectiveness of seismic retrofit to reduce the risk of damage and associated losses (repair costs) of wood-frame houses with cripple wall and sill anchorage deficiencies as well as retrofitted conditions that address those deficiencies. Tasks that support and inform the loss-modeling effort are: (1) collecting and summarizing existing information and results of previous research on the performance of wood-frame houses; (2) identifying construction features to characterize alternative variants of wood-frame houses; (3) characterizing earthquake hazard and ground motions at representative sites in California; (4) developing cyclic loading protocols and conducting laboratory tests of cripple wall panels, wood-frame wall subassemblies, and sill anchorages to measure and document their response (strength and stiffness) under cyclic loading; and (5) the computer modeling, simulations, and the development of loss models as informed by a workshop with claims adjustors. This report is a product of Working Group 3 (WG3), Task 3.1: Selecting and Scaling Ground-motion records. The objective of Task 3.1 is to provide suites of ground motions to be used by other working groups (WGs), especially Working Group 5: Analytical Modeling (WG5) for Simulation Studies. The ground motions used in the numerical simulations are intended to represent seismic hazard at the building site. The seismic hazard is dependent on the location of the site relative to seismic sources, the characteristics of the seismic sources in the region and the local soil conditions at the site. To achieve a proper representation of hazard across the State of California, ten sites were selected, and a site-specific probabilistic seismic hazard analysis (PSHA) was performed at each of these sites for both a soft soil (Vs30 = 270 m/sec) and a stiff soil (Vs30=760 m/sec). The PSHA used the UCERF3 seismic source model, which represents the latest seismic source model adopted by the USGS [2013] and NGA-West2 ground-motion models. The PSHA was carried out for structural periods ranging from 0.01 to 10 sec. At each site and soil class, the results from the PSHA—hazard curves, hazard deaggregation, and uniform-hazard spectra (UHS)—were extracted for a series of ten return periods, prescribed by WG5 and WG6, ranging from 15.5–2500 years. For each case (site, soil class, and return period), the UHS was used as the target spectrum for selection and modification of a suite of ground motions. Additionally, another set of target spectra based on “Conditional Spectra” (CS), which are more realistic than UHS, was developed [Baker and Lee 2018]. The Conditional Spectra are defined by the median (Conditional Mean Spectrum) and a period-dependent variance. A suite of at least 40 record pairs (horizontal) were selected and modified for each return period and target-spectrum type. Thus, for each ground-motion suite, 40 or more record pairs were selected using the deaggregation of the hazard, resulting in more than 200 record pairs per target-spectrum type at each site. The suites contained more than 40 records in case some were rejected by the modelers due to secondary characteristics; however, none were rejected, and the complete set was used. For the case of UHS as the target spectrum, the selected motions were modified (scaled) such that the average of the median spectrum (RotD50) [Boore 2010] of the ground-motion pairs follow the target spectrum closely within the period range of interest to the analysts. In communications with WG5 researchers, for ground-motion (time histories, or time series) selection and modification, a period range between 0.01–2.0 sec was selected for this specific application for the project. The duration metrics and pulse characteristics of the records were also used in the final selection of ground motions. The damping ratio for the PSHA and ground-motion target spectra was set to 5%, which is standard practice in engineering applications. For the cases where the CS was used as the target spectrum, the ground-motion suites were selected and scaled using a modified version of the conditional spectrum ground-motion selection tool (CS-GMS tool) developed by Baker and Lee [2018]. This tool selects and scales a suite of ground motions to meet both the median and the user-defined variability. This variability is defined by the relationship developed by Baker and Jayaram [2008]. The computation of CS requires a structural period for the conditional model. In collaboration with WG5 researchers, a conditioning period of 0.25 sec was selected as a representative of the fundamental mode of vibration of the buildings of interest in this study. Working Group 5 carried out a sensitivity analysis of using other conditioning periods, and the results and discussion of selection of conditioning period are reported in Section 4 of the WG5 PEER report entitled Technical Background Report for Structural Analysis and Performance Assessment. The WG3.1 report presents a summary of the selected sites, the seismic-source characterization model, and the ground-motion characterization model used in the PSHA, followed by selection and modification of suites of ground motions. The Record Sequence Number (RSN) and the associated scale factors are tabulated in the Appendices of this report, and the actual time-series files can be downloaded from the PEER Ground-motion database Portal (https://ngawest2.berkeley.edu/)(link is external).

This Coastal and Hydraulics Engineering Technical Note (CHETN) describes the continuing efforts towards incorporating rapid tidal time-series reconstruction and prediction capabilities into the Coastal Hazards System (CHS) and the Stochastic Storm Simulation System (StormSim). The CHS (Nadal-Caraballo et al. 2020) is a national effort for the quantification of coastal storm hazards, including a database and web tool (https://chs.erdc.dren.mil) for the deployment of results from the Probabilistic Coastal Hazard Analysis (PCHA) framework. These PCHA products are developed from regional studies such as the North Atlantic Coast Comprehensive Study (NACCS) (Nadal-Caraballo et al. 2015; Cialone et al. 2015) and the ongoing South Atlantic Coast Study (SACS). The PCHA framework considers hazards due to both tropical and extratropical cyclones, depending on the storm climatology of the region of interest. The CHS supports feasibility studies, probabilistic design of coastal structures, and flood risk management for coastal communities and critical infrastructure. StormSim (https://stormsim.erdc.dren.mil) is a suite of tools used for statistical analysis and probabilistic modeling of historical and synthetic storms and for stochastic design and other engineering applications. One of these tools, the Coastal Hazards Rapid Prediction System (CHRPS) (Torres et al. 2020), can perform rapid prediction of coastal storm hazards, including real-time hurricane-induced flooding. This CHETN discusses the quantification and validation of the Advanced Circulation (ADCIRC) tidal constituent database (Szpilka et al. 2016) and the tidal reconstruction program Unified Tidal analysis (UTide) (Codiga 2011) in the Puerto Rico and U.S. Virgin Islands (PR/USVI) coastal regions. The new methodology discussed herein will be further developed into the Rapid Tidal Reconstruction (RTR) tool within the StormSim and CHS frameworks.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.