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Forecasting CPI Xiang Huang, Wenjie Huang, Teng Wang, Hong Wang Benjamin Wright, Naiwen Chang, Jake Stamper

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Definition The consumer price index (CPI) measures the cost of a standard basket of goods and services commonly purchased by households. The index is published monthly by the Bureau of Labor Statistics, and is used to calculate the rate of inflation.

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CPI index since 1983 Trace Histogram

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Time Trend Forecast

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Correlogram of CPI Evidence of an evolutionary series. Use first-differencing to pre-whiten and obtain a stationary series.

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First-Difference of CPI Trace Histogram

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C orrelogram of DCPI Add AR(1),AR(2),and MA(12)

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Unit Root of DCPI Augmented Dickey- Fuller is sufficiently negative, rejecting the presence of a unit root.

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ARIMA MODEL OF DCPI Tan theta=0.36/0.28=1.2857 Theta=52.125 degree Cycle=360/52.125=6.9 years Cycle Calculation:

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ARIMA MODEL OF DCPI Actual, Fitted and Residuals Graph Histogram of Residuals

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Correlogram of Residuals Breusch-Godfrey Serial Correlation Test

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Correlogram of Square Residuals Add ARCH(1)

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Add ARCH(1) and GARCH(1) in ARIMA model Correlogram

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Drop AR(2) Trace of the standardized residuals

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Histogram of Standardized Squared Residuals Correlogram of Standardized Squared Residuals

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Exponential Smoothing Forecast Sample: 1 340 Included observations: 340 Method: Single Exponential Original Series: CPI Forecast Series: CPISM Parameters:Alpha0.9990 Sum of Squared Residuals1027.477 Root Mean Squared Error1.738388 End of Period Levels:Mean223.442055779

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Attempt to Create Distributed Lag Model No Granger Causality for Relevant Variables GDP Unemployment Rate Capacity Utilization Industrial Production Manufacturing Production Commercial and Industrial Loans Consumer Loans Consumer Sentiment Money Supply (M2) Federal Funds Rate Without Granger Causality, no distributed lag model could be crated

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Comparison of Different Models MethodForecast of CPI for April 2011 Time Trend Forecast221.89 ARIMA Model224.19 GARCH(1,1) MODEL224.14 Exponential Smoothing223.44 True value CPI in April 2011: 224.43 Actual Value of CPI in April 2011: 224.43

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Forecast for May 2011 CPI Monthly Inflation Rate (Annualized) Point Forecast225.053.37% 95 Percent Confidence Interval 224.22 to 225.88-1.12% to 8.03%

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