# CPI-U monthly

The U.S. Consumer Price Index (CPI) is a time series measure of the price level of consumer goods and services. The Bureau of Labor Statistics, which started the statistic in 1919, publishes the CPI on a monthly basis

The CPI is primarily used as an economic indicator. As the most widely used measure of inflation, the CPI is an indicator of the effectiveness of government fiscal and monetary policy. Especially for inflation targeting monetary policy by the Federal Reserve; however, the Federal Reserve System has recently begun favoring the Personal consumption expenditures price index (PCE) over the CPI as a measure of inflation. Business executives, labor leaders, and other private citizens also use the CPI as a guide in making economic decisions.

### Objective

For our purpose, we analyze, model and forecast the CPI-U levels (and implied inflation rate) using econmetric techniques.

Date Range: 1913 - January 2009

### Preliminary Analysis

Examining the graph for CPI-U levels above, it become obvious that index level follow a non-stationary process, and it is more like random walk (i.e. unit root). To proceed, we convert levels into logarthmic monthly differences using $$r_{t} = \ln(\frac{CPI_{t}}{CPI_{t-1}}) = (1-L)\ln(CPI_{t})$$
Using NumXL and Excel built-in function, we can generate the required time series (i.e. DIFF(log(E2:E711)))

Next, we examine the series descriptive statistic and test the hypothesis whether the log returns are not serially correlated (i.e. white noise):

The log differences are not white noise, and its probabilistic distribution exhibits fat tails than normal distribution.

 ACF PACF

The log returns graph and the correlogram suggest a time varying conditional mean and volatility. An ARMA model for the conditional mean and GARCH-type of process of process for conditional variance may be in order here.