# Minitab Help: Time Series & Autocorrelation

Minitab Help: Time Series & Autocorrelation

## Minitab®

• Select Stat > Time Series > Time Series Plot, select "price" for the Series, click the Time/Scale button, click "Stamp" under "Time Scale" and select "date" to be a Stamp column.
• Select Stat > Time Series > Partial Autocorrelation to create a plot of partial autocorrelations of price.
• Select Calc > Calculator to calculate a lag-1 price variable.
• Create a basic scatterplot of price vs lag1price.
• Perform a linear regression analysis of price vs lag1price (a first-order autoregression model).

## Earthquakes (autoregression model)

• Select Stat > Time Series > Time Series Plot, select "Quakes" for the Series, click the Time/Scale button, click "Stamp" under "Time Scale" and select "Year" to be a Stamp column.
• Select Stat > Time Series > Partial Autocorrelation to create a plot of partial autocorrelations of Quakes.
• Select Calc > Calculator to calculate lag-1, lag-2, and lag-3 Quakes variables.
• Perform a linear regression analysis of Quakes vs the three lag variables (a third-order autoregression model).

## Blaisdell company (regression with autoregressive errors)

• Perform a linear regression analysis of comsales vs indsales (click "Results" to select the Durbin-Watson statistic and click "Storage" to store the residuals).
• Select Stat > Time Series > Autocorrelation and select the residuals; this displays the autocorrelation function and the Ljung-Box Q test statistic.
• Perform the Cochrane-Orcutt procedure:
• Select Calc > Calculator to calculate a lag-1 residual variable.
• Perform a linear regression analysis with no intercept of residuals vs lag-1 residuals (select "Storage" to store the estimated coefficients; the estimated slope, 0.631164, is the estimate of the autocorrelation parameter).
• Select Calc > Calculator to calculate a transformed response variable, Y_co = comsales-0.631164*LAG(comsales,1).
• Select Calc > Calculator to calculate a transformed predictor variable, X_co = indsales-0.631164*LAG(indsales,1).
• Perform a linear regression analysis of Y_co vs X_co.
• Transform the resulting intercept parameter and its standard error by dividing by 1 – 0.631164 (the slope parameter and its standard error do not need transforming).
• Forecast comsales for period 21 when indsales are projected to be \$175.3 million.
• Perform the Hildreth-Lu procedure:
• Select Calc > Calculator to calculate a transformed response variable, Y_h1.1 = comsales-0.1*LAG(comsales,1).
• Select Calc > Calculator to calculate a transformed predictor variable, X_h1.1 = indsales-0.1*LAG(indsales,1).
• Perform a linear regression analysis of Y_h1.1 vs X_h1.1 and record the SSE.
• Repeat steps 1-3 for a series of estimates of the autocorrelation parameter to find when SSE is minimized (0.96 leads to the minimum in this case).
• Perform a linear regression analysis of Y_h1.96 vs X_h1.96.
• Transform the resulting intercept parameter and its standard error by dividing by 1 – 0.96 (the slope parameter and its standard error do not need transforming).
• Perform the first differences procedure:
• Select Calc > Calculator to calculate a transformed response variable, Y_fd = comsales-LAG(comsales,1).
• Select Calc > Calculator to calculate a transformed predictor variable, X_fd = indsales-LAG(indsales,1).
• Perform a linear regression analysis with no intercept of Y_fd vs X_fd.
• Calculate the intercept parameter as mean(comsales) – slope estimate x mean(indsales).

## Metal fabricator and vendor employees (regression with autoregressive errors)

• Perform a linear regression analysis of metal vs vendor (click "Results" to select the Durbin-Watson statistic and click "Storage" to store the residuals).
• Create a fitted line plot.
• Create residual plots and select "Residuals versus order."
• Select Stat > Time Series > Partial Autocorrelation and select the residuals.
• Perform the Cochrane-Orcutt procedure using the above directions for the Blaisdell company example.

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