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 series data is identified and more or less formally described. Once the pattern is established, we can interpret and integrate it with other data (e.g., seasonal commodity prices). Regardless of the depth of our understanding and the validity of our interpretation (theory) of the phenomenon, we can extrapolate the identified pattern to predict future events. Several methods are described in this chapter, along with their strengths and weaknesses. Although most are simple in concept, the computations required to estimate parameters and perform the analysis are tedious enough that computer implementation is essential. The easiest way to identify patterns is to plot the data and examine the resulting graphs. If we did that, what could we observe? There are four basic patters, which are shown in Figure 1.
Any of these patterns, or a combination of them, can be present in a time series of data: 1. Level or horizontal
This pattern exists when data values fluctuate around a constant mean. This is the simplest pattern and easiest to predict. A horizontal pattern is observed when the values of the time series fluctuate around a constant mean. Such time series is also called stationery. In Retail data, stationery time series can be found easily since there are products which sales roughly the same amount of items every period. In the stock market however, it's difficult (if not impossible) to find horizontal patterns. Most of the time series there are non-stationery. Time series with horizontal patterns are very easy to forecast. 2. Trend
When data exhibit an increasing or decreasing pattern over time, we say that they exhibit a trend. The trend can be upward or upward. The trend pattern is straightforward. It consists of a long-term increase or decrease of the values of the time series. Trend patterns are easy to forecast and are very profitable when found by stock traders. 3. Seasonality
Any pattern that regularly repeats itself and is of a constant length is a...
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