Time Series Models
TIME SERIES MODELS Time series analysis provides tools for selecting a model that can be used to forecast of future events.
Time series models are based on the assumption that all information needed to generate a forecast is contained in the time series of data. The forecaster looks for patterns in the data and tries to obtain a forecast by projecting that pattern into the future.
A forecasting method is a (numerical) procedure for generating a forecast. When such methods are not based upon an underlying statistical model, they are termed heuristic.
A statistical (forecasting) model is a statistical description of the data generating process from which a forecasting method may be derived. Forecasts are made by using a forecast function that is derived from the model.
WHAT IS A TIME SERIES?
A time series is a sequence of observations over time. A time series is a sequence of data points, measured typically at successive time instants spaced at uniform time intervals.
A time series is a sequence of observations of a random variable. Hence, it is a stochastic process. Examples include the monthly demand for a product, the annual freshman enrollment in a department of a university, and the daily volume of flows in a river.
Forecasting time series data is important component of operations research because these data often provide the foundation for decision models. An inventory model requires estimates of future demands, a course scheduling and staffing model for a university requires estimates of future student inflow, and a model for providing warnings to the population in a river basin requires estimates of river flows for the immediate future. * TWO MAIN GOALS:
There are two main goals of time series analysis: (a) identifying the nature of the phenomenon represented by the sequence of observations, and (b) forecasting (predicting future values of the time series variable).
Both of these goals require that the pattern of observed time
Time series models are based on the assumption that all information needed to generate a forecast is contained in the time series of data. The forecaster looks for patterns in the data and tries to obtain a forecast by projecting that pattern into the future.
A forecasting method is a (numerical) procedure for generating a forecast. When such methods are not based upon an underlying statistical model, they are termed heuristic.
A statistical (forecasting) model is a statistical description of the data generating process from which a forecasting method may be derived. Forecasts are made by using a forecast function that is derived from the model.
WHAT IS A TIME SERIES?
A time series is a sequence of observations over time. A time series is a sequence of data points, measured typically at successive time instants spaced at uniform time intervals.
A time series is a sequence of observations of a random variable. Hence, it is a stochastic process. Examples include the monthly demand for a product, the annual freshman enrollment in a department of a university, and the daily volume of flows in a river.
Forecasting time series data is important component of operations research because these data often provide the foundation for decision models. An inventory model requires estimates of future demands, a course scheduling and staffing model for a university requires estimates of future student inflow, and a model for providing warnings to the population in a river basin requires estimates of river flows for the immediate future. * TWO MAIN GOALS:
There are two main goals of time series analysis: (a) identifying the nature of the phenomenon represented by the sequence of observations, and (b) forecasting (predicting future values of the time series variable).
Both of these goals require that the pattern of observed time
Bibliography: Box, G.E.P and G.M. Jenkins and G.D. Reinsel, Time Series Analysis, Forecasting, and Control, Third Edition, Prentice Hall, Englewood Cliffs, NJ, 1993. Brockwell, Peter J. and Davis, Richard A. (2002). Introduction to Time Series and Forecasting, 2nd. ed., Springer-Verlang. Chatfield, C., The Analysis of Time Series: An Introduction, Fifth Edition, Chapman &Hall, Boca Raton, FL, 1996. Fuller, W.A., Introduction to Statistical Time Series, Second Edition, John Wiley & Sons, New York, 1996. (Electronic Version): StatSoft, Inc. (2012). Electronic Statistics Textbook. Tulsa, OK: StatSoft. WEB: http://www.statsoft.com/textbook/. (Printed Version): Hill, T. & Lewicki, P. (2007). STATISTICS: Methods and Applications. StatSoft, Tulsa, OK.