Fitting Time Series Models Research Articles

Short Term Load Forecasting Using Curve Fitting Prediction Optimized By Bacterial Foraging Optimization

Short term load forecast plays an important role in electric power system planning, design and operation. Curve fitting prediction technique and time series models are used for hourly loads forecasting of the week days. In this paper a new approach for short-term load forecasting is introduced. This approach is curve fitting prediction technique combined with Bacterial Foraging optimization. BFO is used to get optimum parameters of the model describing the system with minimum error between actual and forecasted load. The suitability of the proposed approach is illustrated through an application to the actual load data of New England control area.

Using Iterative linear regression model to time series models

In this paper we introduced a new method for fitting time series models, we called it “iterated linear regression” method. A comparison between the classical linear regression, iterated linear regression and Box-Jenkins methods using real data such as airline data and sunspot numbers is proposed.

Editorial: Special issue on time series analysis in the biological sciences

Editorial: Special issue on time series analysis in the biological sciences

Short-Term Load Forecasting Using Curve Fitting Prediction Optimized by Genetic Algorithms

This paper presents a new approach for short-term load forecasting (STLF). Curve fitting prediction and time series models are used for hourly loads forecasting of the week days. The curve fitting prediction (CFP) technique combined with genetic algorithms (GAs) is used for obtaining the optimum parameters of Gaussian model to obtain a minimum error between actual and forecasted load. A new technique for selecting the training vectors is introduced. The proposed model is simple, fast, and accurate. It is shown that the proposed approach provide very accurate hourly load forecast. Also it is shown that the proposed method can provide more accurate results than the conventional techniques. The mean percent relative error of the model is less than 1 %.

Fitting of Time Series Models to Forecast Streamflow and Groundwater Using Simulated Data from Swat

Time series models provide a valuable tool for simulation and forecasting hydrologic variables. However, time series models require fitting long series of records. This study explores the applicability of soil water assessment tool SWAT, a deterministic hydro- logic model, to generate long data series to fit autoregressive and autoregressive moving average models, in order to perform short-term forecasting of monthly streamflow and groundwater table depth in areas that lack long historical records. SWAT performed well in reproducing the statistical structure of the variables making it possible to fit time series models to simulated series. Time series models fitted to SWAT simulated data and to historical records showed a similar but poor performance to forecast monthly streamflow in all watersheds. However, time series fitted to SWAT data for groundwater table depth showed good performance for forecasting this variable with correlation coefficients between 0.58 to 0.70 and Nash-Sutcliffe model efficiencies from 0.22 to 0.46 in the validation period.

Max-Chart for Autocorrelated Processes

Statistical process control procedures are usually implemented under the assumption that the observations from a process are independent over time. However, this assumption is often violated. Therefore, we propose a single Shewhart-type control chart for autocorrelated process by fitting a time series model into the process and monitoring the residuals from the forecast values of a fitted time series model. Numerical results illustrate the ARL of the AR (1) plus random error model, for the cases of step changes in the mean and/or standard deviation. Compared to other charts that monitor autocorrelated processes, this chart quickly detects shifts in the process location and spread particularly for large shifts.

Analysis of Software Aging in a Web Server

Several recent studies have reported & examined the phenomenon that long-running systems show an increasing failure rate and/or a progressive degradation of their performance. Causes of this phenomenon, which has been referred to as software are the accumulation of internal error conditions, and the depletion of operating system resources. A proactive technique called software has been proposed as a way to counteract aging. It involves occasionally terminating the application, cleaning its internal state and/or its environment, and then restarting it. Due to the costs incurred by rejuvenation, an important question is when to schedule this action. While periodic rejuvenation at constant time intervals is straightforward to implement, it may not yield the best results. The rate at which ages is usually not constant, but it depends on the time-varying system workload. Software rejuvenation should therefore be planned & initiated in the face of the actual system behavior. This requires the measurement, analysis, and prediction of system resource usage. In this paper, we study the development of resource usage in a web server while subjecting it to an artificial workload. We first collect data on several system resource usage & activity parameters. Non-parametric statistical methods are then applied toward detecting & estimating trends in the data sets. Finally, we fit time series models to the data collected. Unlike the models used previously in the research on aging, these time series models allow for seasonal patterns, and we show how the exploitation of the seasonal variation can help in adequately predicting the future resource usage. Based on the models employed here, proactive management techniques like rejuvenation triggered by actual measurements can be built

Fitting time series models for longitudinal survey data under informative sampling

The purpose of this paper is to account for informative sampling in fitting time series models, and in particular an autoregressive model of order one, for longitudinal survey data. The idea behind the proposed approach is to extract the model holding for the sample data as a function of the model in the population and the first-order inclusion probabilities, and then fit the sample model using maximum-likelihood, pseudo-maximum-likelihood and estimating equations methods. A new test for sampling ignorability is proposed based on the Kullback–Leibler information measure. Also, we investigate the issue of the sensitivity of the sample model to incorrect specification of the conditional expectations of the sample inclusion probabilities. The simulation study carried out shows that the sample-likelihood-based method produces better estimators than the pseudo-maximum-likelihood method, and that sensitivity to departures from the assumed model is low. Also, we find that both the conventional t-statistic and the Kullback–Leibler information statistic for testing of sampling ignorability perform well under both informative and noninformative sampling designs.

Evaluation of groundwater availability and sustainable extraction rate for the Upper Santiago Valley Aquifer, Chile

The use of groundwater as water supply has increased dramatically in Santiago, Chile, during the last decades, and there is a need for accurately estimating the actual groundwater supply capacity in the upper Santiago Valley aquifer. The behavior of this aquifer was studied in order to determine the availability of water and the long-range sustainable extraction rate. Water-table depths were simulated using a numerical model with information on recharge from the last 48 years under different extraction policies. With this series of groundwater level data, groundwater level probability distribution functions were determined and extraction statistics were estimated by fitting time series models and by using the crossing theory. With this information, it has been possible to calculate the risk of being unable to supply groundwater demand because the results verify that only 67% of the water rights granted are able to be extracted on a sustained basis with a 90% exceedance probability. Furthermore, the results obtained demonstrate that the method is adequate for determining exceedance probabilities of groundwater flow.

A test for multivariate structure

We present a test for detecting 'multivariate structure' in data sets. This procedure consists of transforming the data to remove the correlations, then discretizing the data and, finally, studying the cell counts in the resulting contingency table. A formal test can be performed using the usual chi-squared test statistic. We give the limiting distribution of the chi-squared statistic and also present simulation results to examine the accuracy of this limiting distribution in finite samples. Several examples show that our procedure can detect a variety of different types of structure. Our examples include data with clustering, digitized speech data, and residuals from a fitted time series model. The chi-squared statistic can also be used as a test for multivariate normality.

Control Charts for Monitoring the Mean and Variance of Autocorrelated Processes

In statistical process control it is usually assumed that the observations taken from the process of interest are independent, but in practice the observations in many cases are actually autocorrelated. This paper considers the problem of monitoring a process in which the observations can be represented as a first-order autoregressive process plus a random error. The problem of detecting special causes which may produce changes in the process mean and/or variance is considered. Several types of control charts and combinations of control charts are evaluated for their ability to detect changes in the process mean and variance. Some of these control charts plot the original observations and have control limits adjusted to account for the autocorrelation in the observations, and others plot the residuals from the forecast values of a fitted time series model. The results of these investigations show that there is no combination of charts that gives optimal performance across a wide variety of situations, but, for reasonably good overall performance, an exponentially weighted moving average chart of the observations used with a Shewhart chart of the residuals can be recommended for practical applications.

Monitoring clean room air using Cuscore charts

In many process monitoring situations where the data are collected over time, the measurements tend to be autocorrelated. In those cases one can fit a time series model to the data to account for the autocorrelation. Once a model has been fitted, it can be used to predict the behaviour of the process, and the residuals can be used to monitor the process using e.g., a Shewhart or Cusum chart. Two issues that are often overlooked when fitting time series models and using the residuals for process monitoring are (i) the validity of the underlying assumption that the time series model fitted to the data will also fit future observations reasonably well, and (ii) that its parameters will remain fairly constant. Either of these assumptions, or both, might not hold, which in turn will affect the performance of the monitoring scheme. In this paper we show how Cuscore charts can be used to check these assumptions by detecting changes in the parameters of an integrated moving average (IMA) model used to monitor the air quality in a clean room environment. The Cuscore can also be effectively used to detect non-stationarity in time series data as well as departures from a state of statistical control. © 1998 John Wiley & Sons, Ltd.

Monitoring clean room air using Cuscore charts

In many process monitoring situations where the data are collected over time, the measurements tend to be autocorrelated. In those cases one can fit a time series model to the data to account for the autocorrelation. Once a model has been fitted, it can be used to predict the behaviour of the process, and the residuals can be used to monitor the process using e.g., a Shewhart or Cusum chart. Two issues that are often overlooked when fitting time series models and using the residuals for process monitoring are (i) the validity of the underlying assumption that the time series model fitted to the data will also fit future observations reasonably well, and (ii) that its parameters will remain fairly constant. Either of these assumptions, or both, might not hold, which in turn will affect the performance of the monitoring scheme. In this paper we show how Cuscore charts can be used to check these assumptions by detecting changes in the parameters of an integrated moving average (IMA) model used to monitor the air quality in a clean room environment. The Cuscore can also be effectively used to detect non-stationarity in time series data as well as departures from a state of statistical control. © 1998 John Wiley & Sons, Ltd.

Fitting time series models to nonstationary processes

A general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation. The asymptotic properties of the estimate are derived under the assumption of possible model misspecification. For autoregressive processes with time varying coefficients, the estimate is compared to the least squares estimate. Furthermore, the behavior of estimates is explained when a stationary model is fitted to a nonstationary process.

Fitting Time Series Models by Minimizing Multistep-ahead Errors: A Frequency Domain Approach

Summary This paper brings together two topics in the estimation of time series forecasting models: the use of the multistep-ahead error sum of squares as a criterion to be minimized and frequency domain methods for carrying out this minimization. The methods are developed for the wide class of time series models having a spectrum which is linear in unknown coefficients. This includes the IMA(1, 1) model for which the common exponentially weigh-ted moving average predictor is optimal, besides more general structural models for series exhibiting trends and seasonality. The method is extended to include the Box–Jenkins ‘air line' model. The value of the multistep criterion is that it provides protection against using an incorrectly specified model. The value of frequency domain estimation is that the iteratively reweighted least squares scheme for fitting generalized linear models is readily extended to construct the parameter estimates and their standard errors. It also yields insight into the loss of efficiency when the model is correct and the robustness of the criterion against an incorrect model. A simple example is used to illustrate the method, and a real example demonstrates the extension to seasonal models. The discussion considers a diagnostic test statistic for indicating an incorrect model.

A statistic to check model adequacy in time series

A simple statistic is suggested to examine if the assumptions on variances in a fitted time series model is valid or not. The properties of the statistic are discussed and examples are considered.

Continuous Time Series Models for Unequally Spaced Data Applied to Modeling Atomic Clocks

State space representations and Kalman filters used to calculate likelihoods have increased the ease and flexibility of fitting time series models to data. When data are unequally spaced with no underlying basic sampling interval, continuous time series models are more natural than discrete time series models. State space representations still provide the flexibility needed to include a large class of models. This paper gives a survey of state space methods for continuous time processes, discusses extensions to multivariate data at unequally spaced time points with missing data within the observation vector, and gives an example of estimating time and model parameters from an ensemble of atomic clocks.

Utility Operating Strategy and Requirements for Wind Power Forecast

The unit commitment of a generation system including a significant number of wind energy conversion systems will be based on wind power forecasts which will themselves be based on wind speed forecasts. Forecasts for periods of equal length with the startup/shutdown times of conventional units will be of great importance. The problem of getting good wind speed forecasts is investigated by fitting time series models to wind speed data. In this paper, the investigations are confined to projection times up to 3 and 6 h. In addition, the impact of hypothetical perfect wind power forecasts on the commitment of intermediate load units is indicated by calculations of the wind power variations within periods of up to 3 h.

On the stationarity of multiple autoregressive approximants: theory and algorithms

Numerical methods are presented for determining the stability of a multiple autoregressive scheme. The question of stability is important in prediction theory, and the methods for determining stability are such that they yield information which is very useful for fitting time series models to data.

Fitting Time Series Models for Prediction

The mathematical theory of the best linear prediction of stationary time series presumes that the model generating the series, which can be specified by either the autocovariance function or the spectral density, is known. The true model is, of course, not known in practice, and the procedure is to fit a model and predict as if this fitted model were the truth. The question then is one of deciding whether the resulting predictions are about as good as could be gotten if the truth were known. This paper describes a method for assessing the predictions of the fitting model by an analysis of residuals. In particular, it is argued that the traditional tests of hypothesis for white noise are inappropriate if prediction is the goal, and a method is described for determining whether or not the mean square errors of the predictions arising from the fitted model can be measurably reduced.