Analysis and Forecasting of Selected Crop and Livestock Time Series in Louisiana (Box-Jenkins).

This study utilizes the Regression, Exponential Smoothing, Census X-11 and Box-Jenkins techniques to simulate the historical time series on selected livestock and crop prices and quantities in Louisiana. The data period covered was from 1972 through 1983 for the monthly time series, and from 1924 through 1983 for the annual time series. The price and production situation for the selected time series was also reviewed for the period 1972-1983. The variability among and within the selected time series was also evaluated. The methodology in this study provided a blend of economic and statistical frameworks. The economic framework provided the medium for explaining how the time series components--trend, seasonal, cyclical and irregular--contribute to the overall variation in any given time series. The statistical framework reinforced the economic framework quantitatively. It was evident from the review of the agricultural situation in Louisiana for the period 1972-1983 that both cyclical, seasonal and irregular factors have changed with the general trend underlying the agricultural series considered in this analysis. It was also found that over the years, livestock prices in Louisiana have had a larger relative variation than crop prices--except for sweet potatoes. Among the crops, soybean prices were the least variable. By utilizing some measures of accuracy statistics to evaluate the ex-post forecast estimates generated by the forecasting techniques, it was found that the Box-Jenkins technique consistently out-performed the other techniques. For seasonal adjustment purposes, the Census X-11 and exponential smoothing provided better seasonally adjusted estimates than the regression procedure. However, in both the seasonal adjustment and forecasting evaluations, unique contributions were realized from each technique, for some of the selected time series. Combined forecasting provided the minimum mean squared error estimates for at least 94 percent of the monthly and annual data studied

Forecasting electricity load demand using hybrid exponential smoothing-artificial neural network model

Short-term electricity load demand forecast is a vital requirements for power systems. This research considers the combination of exponential smoothing for double seasonal patterns and neural network model. The linear version of Holt-Winter method is extended to accommodate a second seasonal component. In this work, the Fourier with time varying coefficient is presented as a means of seasonal extraction. The methodological contribution of this paper is to demonstrate how these methods can be adapted to model the time series data with multiple seasonal pattern, correlated non stationary error and nonlinearity components together. The proposed hybrid model is started by implementing exponential smoothing state space model to obtain the level, trend, seasonal and irregular components and then use them as inputs of neural network. Forecasts of future values are then can be obtained by using the hybrid model. The forecast performance was characterized by root mean square error and mean absolute percentage error. The proposed hybrid model is applied to two real load series that are energy consumption in Bawen substation and in Java-Bali area. Comparing with other existing models, results show that the proposed hybrid model generate the most accurate forecas

Pemodelan Tingkat Suku Bunga Surat Perbendaharaan Negara 3 Bulan

One of the basic macroeconomic assumptions that is still experiencing difficulties developing an accurate economic model is the 3-month Treasury bill (Surat Perbendaharaan Negara/SPN). This is mainly caused by its irregular data period, based on the average yield won in an auction held at a certain period. This study aims to build 3-month Treasury Bill (SPN) interest rate models by comparing several time-series methods, namely spline smoothing, exponential smoothing, moving average smoothing, and a regression model using s spread with one year Government Bond yield (Surat Utang Negara/SUN). This study shows that the spline smoothing method and regression analysis with one year SUN is the best model. In contrast, spline smoothing is better for short-term projections, and regression with one year SUN is better for medium-term projection

Metody pro periodické a nepravidelné časové řady

Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicityNázev práce: Metody pro periodické a nepravidelné časové řady Autor: Mgr. Tomáš Hanzák Katedra: Katedra pravděpodobnosti a matematické statistiky Vedoucí disertační práce: Prof. RNDr. Tomáš Cipra, DrSc. Abstrakt: Disertační práce se primárně zabývá modifikacemi metod typu exponenciální vyrovnávání pro jednorozměrné časové řady s periodicitou a/nebo určitými typy nepravidelností. Je navržena modifikovaná Holtova metoda pro nepravidelné časové řady robustní vůči problému "časově blízkých" pozorování. Obecný koncept modelování sezónnosti je zaveden do Holtovy-Wintersovy metody včetně lineární interpolace sezónních indexů a použití goniometrických funkcí jako speciálních případů (obě metody jsou použitelné pro nepravidelná pozorování). Je zkoumán DLS odhad regrese s lineárním trendem a sezónními indexy a metoda je porovnána s aditivní Holtovou-Wintersovou metodou. Autokorelovaný člen je navržen jako další složka dekompozice časové řady. Navržené metody jsou porovnávány s klasickými na reálných datech a/nebo prostřednictvím simulačních studií. Klíčová slova: Diskontované nejmenší čtverce, exponenciální vyrovnávání, Holtova-Wintersova metoda, nepravidelná pozorování, periodicita časových řadKatedra pravděpodobnosti a matematické statistikyDepartment of Probability and Mathematical StatisticsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Exponential Smoothing for Inventory Control: Means and Variances of Lead-Time Demand

Exponential smoothing is often used to forecast lead-time demand for inventory control. In this paper, formulae are provided for calculating means and variances of lead-time demand for a wide variety of exponential smoothing methods. A feature of many of the formulae is that variances, as well as the means, depend on trends and seasonal effects. Thus, these formulae provide the opportunity to implement methods that ensure that safety stocks adjust to changes in trend or changes in season.Forecasting; inventory control; lead-time demand; exponential smoothing; forecast variance.

Automatic forecasting with a modified exponential smoothing state space framework

A new automatic forecasting procedure is proposed based on a recent exponential smoothing framework which incorporates a Box-Cox transformation and ARMA residual corrections. The procedure is complete with well-defined methods for initialization, estimation, likelihood evaluation, and analytical derivation of point and interval predictions under a Gaussian error assumption. The algorithm is examined extensively by applying it to single seasonal and non-seasonal time series from the M and the M3 competitions, and is shown to provide competitive out-of-sample forecast accuracy compared to the best methods in these competitions and to the traditional exponential smoothing framework. The proposed algorithm can be used as an alternative to existing automatic forecasting procedures in modeling single seasonal and non-seasonal time series. In addition, it provides the new option of automatic modeling of multiple seasonal time series which cannot be handled using any of the existing automatic forecasting procedures. The proposed automatic procedure is further illustrated by applying it to two multiple seasonal time series involving call center data and electricity demand data.Exponential smoothing, state space models, automatic forecasting, Box-Cox transformation, residual adjustment, multiple seasonality, time series

The State Space Models Toolbox for MATLAB

State Space Models (SSM) is a MATLAB toolbox for time series analysis by state space methods. The software features fully interactive construction and combination of models, with support for univariate and multivariate models, complex time-varying (dy- namic) models, non-Gaussian models, and various standard models such as ARIMA and structural time-series models. The software includes standard functions for Kalman fil- tering and smoothing, simulation smoothing, likelihood evaluation, parameter estimation, signal extraction and forecasting, with incorporation of exact initialization for filters and smoothers, and support for missing observations and multiple time series input with com- mon analysis structure. The software also includes implementations of TRAMO model selection and Hillmer-Tiao decomposition for ARIMA models. The software will provide a general toolbox for time series analysis on the MATLAB platform, allowing users to take advantage of its readily available graph plotting and general matrix computation capabilities.

Which univariate time series model predicts quicker a crisis? The Iberia case

In this paper four univariate models are fitted to monthly observations of the number of passengers in the Spanish airline IBERIA from January 1985 to October 1994. During the first part of the sample, the series shows an upward trend which has a rupture during 1990 with the slope changing to be negative. The series is also characterized by having seasonal variations. We fit a deterministic components model, the Holt-Winters algorithm, an ARIMA model and a structural time series model to the observations up to December 1992. Then we predict with each ofthe models and compare predicted with observed values. As expected, the results show that the detenninistic model is too rigid in this situation even if the within-sample fit is even better than for any of the other models considered. With respect to Holt-Winters predictions, they faH because they are not able to accornmodate outliers. Finally, ARIMA and structural models are shown to have very similar prediction performance, being flexible enough to predict reasonably well when there are changes in trend