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Time Series Analysis and Forecasting
Many types of data are collected over time. Stock prices, sales volumes, interest rates, and quality measurements are typical examples. Because of the sequential nature of the data, special statistical techniques that account for the dynamic nature of the data are required.
STATGRAPHICS Centurion provides an extensive set of procedures designed for analyzing time series data:
1. Descriptive Methods - time sequence plots, autocorrelation functions, partial autocorrelation functions, periodograms, and cross-correlation functions are all important tools for characterizing time series data.
2. Smoothing - a variety of smoothers are available to estimate the underlying trend in a time series.
3. Seasonal Decomposition - decomposes time series data into trend, cycle, seasonal, and irregular components, and returns seasonally adjusted data if desired.
4. Forecasting - creation of forecasts beyond the end of the data, using trend models, moving averages, exponential smoothers, or ARIMA models.
5. Automatic Forecasting - selects the best forecasting method for a time series by optimizing a specified information criterion.
Characterizing a time series involves estimating not only a mean and standard deviation but also the correlations between observations separated in time. Tools such as the autocorrelation function are important for displaying the manner in which the past continues to affect the future. Other tools, such as the periodogram, are useful when the data contain oscillations at specific frequencies.
When a time series contains a large amount of noise, it can be difficult to visualize any underlying trend. Various linear and nonlinear smoothers are provided to separate the signal from the noise.
When the data contain a strong seasonal effect, it is often important to separate the seasonality from the other components in the time series. This enables one to estimate the seasonal patterns and to generate seasonally adjusted data.
A common goal of time series analysis is extrapolating past behavior into the future. The STATGRAPHICS forecasting procedures include random walks, moving averages, trend models, simple, linear, quadratic, and seasonal exponential smoothing, and ARIMA parametric time series models. Users may compare various models by withholding samples at the end of the time series for validation purposes.
If desired, users may elect to let STATGRAPHICS select a forecasting model for them by comparing multiple models and automatically picking the model that maximizes a specified information criterion. The available criteria are based on the mean squared forecast error, penalized for the number of model parameters that must be estimated from the data. A common use of this procedure in Six Sigma is to select an ARIMA model on which to base an ARIMA control chart, which unlike most control charts does not assume independence between successive measurements. In such cases, the analyst may elect to consider only models of the ARMA(p,p-1) form, which theory suggests can characterize many dynamic processes.
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