Seasonal Autoregressive Moving-average Models Research Articles

One week hourly electricity load forecasting using Neuro-Fuzzy and Seasonal ARIMA models

This paper presents a comparative study of two forecast models for electric load data from Hanoi city, Vietnam. These two forecast models based on the methodology Adaptive Network Based Fuzzy Inference System (ANFIS) and Seasonal Auto Regressive Moving Average (SARIMA). The criteria of performance evaluation are computed to estimate and compare the SARIMA and ANFIS models. The results indicate in our case a preference for the SARIMA model.

Seasonal ARIMA model for generation and forecasting evapotranspirtion of Solapur district of Maharashtra

This paper deals with the stochastic modeling of weekly reference crop evapotranspiration in semi-arid climatic condition by using seasonal Auto Regressive Moving Average (ARIMA) model. The weekly values of reference crop evapotranspiration (ETr) estimated by Penman Monteith method for 23 years (1984 to 2006) were used to fit the ARIMA models of different orders. ARIMA models up to 1st order were selected based on autocorrelation function (ACF) and partial autocorrelation function (PACF) of the ETr series. The parameters of the selected models were obtained with the help of maximum likelihood method. The ARIMA models that satisfied the adequacy tests were selected for forecasting. One year ahead forecast (i.e. for 2007) of ETr values were obtained with the help of these selected models. The root mean square error (RMSE) was computed between forecast and actual values of ETr of 2007. The lowest RMSE was obtained for ARIMA (1,1,0) (1,0,1)52 and hence is the best stochastic model for generating and forecasting of weekly ETr values.

Forecasting Network Traffic Load Using Wavelet Filters and Seasonal Autoregressive Moving Average Model

A computer network's performance can be improved by increasing servers, upgrading the hardware, and gaining additional bandwidth. Another important issue to increase network performance is to use an appropriate mathematical model and using that model for forecasting the network load at peak hours. We analyze a network traffic time series of Internet requests made to a workstation. This series exhibits a long-range dependence and self-similarity in large time scale and exhibits multi-fractal in small time scale. With the growing demand of using computer networks, there is increasing demand to explore new techniques for forecasting. In this paper we used the wavelet filters based on multi-resolution analysis along with the Seasonal Autoregressive Moving Average (SARIMA) models for forecasting network traffic volume. We used the Daubechies 4 (db4) wavelet filters for compression of time series and SARIMA modeling for forecasting the series. Our proposed methodology is based on the theory that most of the network traffic signals are always having the noise and unnecessary details not required for further analysis hence forecasting directly from such signals may prove computationally intensive and prone to error. The denoised and compressed signals using wavelet filters will be comparatively more smoothed and helpful for speedy and accurate forecasts. We compare our results with simple SARIMA methodology and conclude that our proposed method give better and accurate forecasts. Using wavelet based SARIMA model, we believe that with the right choice of mother wavelet, moving towards a wavelet based forecasting system would significantly improve the forecasting efficiency.

On the expectation of estimators for general ARMA processes

A simple technique is presented for obtaining explicit expressions for the approximate expectation of estimators for general stationary autoregressive moving average (ARMA) processes. The technique is based on a Taylor series expansion of the log-likelihood function in terms of the expected values of the sample autocovariances or in terms of the expected value of the periodogram ordinates, depending upon whether the estimation makes use of time-domain methods. For illustrative purpose the expectation of estimators arising from two particular approximations of the likelihood function is obtained , although the proposed technique can be easily extended to other types of log-likelihood functions as well. The results may be used to provide information about the bias of estimators in non-seasonal and seasonal ARMA models.

Parsimony, Model Adequacy and Periodic Correlation in Time Series Forecasting

The merits of the modelling philosophy of Box \& Jenkins (1970) are illustrated with a summary of our recent work on seasonal river flow forecasting. Specifically, this work demonstrates that the principle of parsimony, which has been questioned by several authors recently, is helpful in selecting the best model for forecasting seasonal river flow. Our work also demonstrates the importance of model adequacy. An adequate model for seasonal river flow must incorporate seasonal periodic correlation. The usual autoregressive-moving average (ARMA) and seasonal ARMA models are not adequate in this respect for seasonal river flow time series. A new diagnostic check, for detecting periodic correlation in fitted ARMA models is developed in this paper. This diagnostic check is recommended for routine use when fitting seasonal ARMA models. It is shown that this diagnostic check indicates that many seasonal economic time series also exhibit periodic correlation. Since the standard forecasting methods are inadequate on this account, it can be concluded that in many cases, the forecasts produced are sub-optimal. Finally, a limitation of the arbitrary combination of forecasts is also illustrated. Combining forecasts from an adequate parsimonious model with an inadequate model did not improve the forecasts whereas combining the two forecasts of two inadequate models did yield an improvement in forecasting performance. These findings also support the model building philosophy of Box \& Jenkins. The non-intuitive findings of Newbold \& Granger (1974) and Winkler \& Makridakis (1983) that the apparent arbitrary combination of forecasts from similar models will lead to forecasting performance is not supported by our case study with river flow forecasting.

A note on Kalman filtering for the seasonal moving average model

In recent years, the Kalman filter has been used extensively to compute the exact likelihood of autoregressive-moving average (ARMA) and autoregressive integrated moving average (ARIMA) time series models. See, for example, Akaike (1978), Gardner, Harvey & Phillips (1980), Jones (1980) and Harvey & Pierse (1984). Using the Cholesky factorization, Ansley (1979) gave an alternative computationally efficient algorithm for computing the likelihood of an ARMA model when there are no missing observations. In particular, he showed how to obtain substantial computational savings for the seasonal moving average model by using the Cholesky factorization. By applying his Theorem 4-1, we can obtain similar savings for an algorithm based on the Kalman filter. An extension of the result to a seasonal ARMA model is also given. We consider the zero mean seasonal moving average model

Duality and other properties of multiplicative seasonal autoregressive-moving average models

Model duality is defined between four models referred to as the primal, the dual, the autoregressive adjoint and the moving average adjoint. A duality theorem which generalizes the results of Box & Pierce (1970) and Pierce (1970) is presented. Applications of this duality theorem to autoregressive-moving average models and multiplicative seasonal autoregressive-moving average models are discussed. These applications include: (i) a convenient method for calculating the covariance matrix of the estimated parameters; (ii) convenient formulae for the variances of the residual autocorrelations; (iii) the distribution of the inverse partial autocorrelations. Finally, a useful approximation to the covariance determinant of multiplicative seasonal models is derived.