After last week’s post, I worked on the predictor for the direction of CPI. I’ll start with the construction of the predictor and then move on to the construction of the test.
The construction of the predictor uses the eight components of the CPI as factors. Two values are generated for each factor — the current year-over-year change in the price index and the previous year’s year-over-year change in the price index. These two numbers are compared with those showing an increase being included in the result.
Let’s use Medical Care as an example. From January 2014 to January 2015, the price index changed from 429.621 to 440.969. Then from January 2015 to January 2016, the price index changed from 440.969 to 454.175. This is an increase of 2.64% to 2.99%. Because the year-over-year price index showed a year-over-year increase in the percentage rate of change, the weight of the factor is included in the January 2016 result. Medical Care for January 2016 has a weight of 8.375.
Five of the eight factors showed a year-over-year increase in the percentage rate of change and their combined weights are 39.614. This number has been increasing since June of 2015 when the weighting result was 0.0.
The weighted year-over-year change of those factors showing a year-over-year percentage increase is 0.79%. This modest amount is nowhere near the Federal Reserve’s 2% target, but it is an increase from December’s reading of -1.32% (the Transportation factor had an unusual impact on the final result).
The test that I created was to compare the correlation of the result to the subsequent month’s annualized ten-year CPI percentage change. The hypothesis was an increase or decrease in the size of the weights in the result would cause an increase or decrease in the following month’s ten-year annualized CPI price change (this is purposefully worded to show the expectation of a positive correlation).
The correlation showed a positive result of 0.6655. Constructing the test statistic resulted in 4.4576. The 95% confidence interval of a two-tailed T test gave a critical T value of 2.0595. Since the test statistic is greater than the critical value, the null hypothesis can be rejected and there is sufficient evidence the predictor does lead to a change in the ten-year price change.
Using this data and calculating the test could not have been done without the class I am teaching this quarter — Introduction to Business Statistics. I know the students are wondering why they need to take this on the journey to their Business degree, but the logic of constructing a hypothesis and test will serve them later.