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MITOCW | watch?v=9G1IDAqrWkg The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: We introduced the data last time. These were some macroeconomic variables that can be used for forecasting the economy in terms of growth and factors such as inflation or unemployment. The case note goes through analyzing just three of these economic time series-- the unemployment rate, the federal funds rate, and a measure of the CPI, or Consumer Price Index. When one fits vector autoregression model to this data, it turns out that the roots of the characteristic polynomial are 1.002, then 0.9863. And you recall when our discussion of vector autoregressive models, there's a characteristic equation sort of in matrix form, the determinant is just like the univariate autoregressive case. And in order for the process to be invertible, basically, the roots of the characteristic polynomial need to be less than 1 in magnitude. In this implementation of the vector autoregression model, the characteristic roots are the inverses of the characteristic roots that we've been discussing. So anyway, this particular fit of the vector autoregression model suggests that the process is non-stationary. And so one should be considering different series to model this as a stationary time series. But in terms of interpreting the regression model, one can see-- to accommodate the non-stationarity, we can take differences of all the series and fit the vector autoregressive to the difference series. So one way of eliminating any non- stationarity and time series models, basically and eliminate the random walk aspect of the processes is to be modeling first differences. And so doing that with this series-- let's see. Here is just a graph of the time series properties of the different series. So with our original series, we take differences and 1
eliminate missing values in this r code. And this autocorrelation function shows us basically the correlations and auto correlations of individual series and the cross correlations across the different series. So along the diagonals are the autocorrelation function. And one can see that every series is correlation one with itself. But then at the first lag positive for the Fed funds and the CPI measured. And there's also some cross correlations that are strong. And whether or not a correlation is strong or not depends upon how much uncertainty there is in our estimate of the correlation. And these dashed lines here correspond to plus or minus two standard deviations of the correlation coefficient when the correlation coefficient is equal to 0. So any correlations that sort of go beyond those bounds is statistically significant. The partial autocorrelation function is graphed here.

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• Spring '17
• Jim Angel

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