Forecasting CPI

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

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.

CPI index since 1983

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CPI

Trace Histogram

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Series: CPISample 1 340Observations 340

Mean 158.9701Median 159.7500Maximum 224.4330Minimum 97.90000Std. Dev. 36.57263Skewness 0.045908Kurtosis 1.864855

Jarque-Bera 18.37395Probability 0.000102

Time Trend Forecast

Correlogram of CPI

Evidence of an

evolutionary series.

Use first-differencing to pre-whiten and obtain a stationary series.

First-Difference of CPI Trace Histogram

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DCPI

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Series: DCPISample 1 340Observations 339

Mean 0.373254Median 0.400000Maximum 2.700000Minimum -3.928000Std. Dev. 0.481705Skewness -2.153560Kurtosis 25.06468

Jarque-Bera 7138.795Probability 0.000000

Correlogram of DCPI

AddAR(1),AR(2),and

MA(12)

Unit Root of DCPI

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

ARIMA MODEL OF DCPI

Tan theta=0.36/0.28=1.2857Theta=52.125 degreeCycle=360/52.125=6.9 years

Cycle Calculation:

ARIMA MODEL OF DCPI

Actual, Fitted and Residuals Graph

Histogram of Residuals

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Residual Actual Fitted

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Series: ResidualsSample 4 340Observations 337

Mean 4.09e-05Median -0.024544Maximum 2.109857Minimum -2.862702Std. Dev. 0.413371Skewness -1.009439Kurtosis 14.32945

Jarque-Bera 1859.569Probability 0.000000

Correlogram of Residuals Breusch-Godfrey

Serial Correlation Test

Correlogram of Square Residuals

Add ARCH(1)

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

Correlogram

Drop AR(2)

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SDRESID

Trace of the standardized residuals

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Series: SDRESIDSample 1 340Observations 338

Mean 0.044213Median -0.031016Maximum 4.034350Minimum -3.266398Std. Dev. 1.000513Skewness 0.540747Kurtosis 4.851605

Jarque-Bera 64.75614Probability 0.000000

Histogram of Standardized Squared Residuals

Correlogram of Standardized Squared Residuals

Exponential Smoothing ForecastSample: 1 340

Included observations: 340

Method: Single Exponential

Original Series: CPI

Forecast Series: CPISM

Parameters: Alpha 0.9990

Sum of Squared Residuals 1027.477

Root Mean Squared Error 1.738388

End of Period Levels: Mean 223.442055779

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

Comparison of Different ModelsMethod Forecast of CPI for April 2011

Time Trend Forecast 221.89

ARIMA Model 224.19

GARCH(1,1) MODEL 224.14

Exponential Smoothing 223.44

True value CPI in April 2011: 224.43True value CPI in April 2011: 224.43

Actual Value of CPI in April 2011: 224.43

Forecast for May 2011

CPI Monthly Inflation Rate (Annualized)

Point Forecast 225.05 3.37%

95 Percent Confidence Interval 224.22 to 225.88 -1.12% to 8.03%