Local Trend Kalman Filter
Don't follow trends, start trends. Frank Capra I have to tell you about the Kalman filter, because what it does is pretty damn amazing. Tim Babb In a previous post , I looked at an application of a Kalman filter for simple projectile motion. In this post, I'll explore a different use of the Kalman filter, analyzing the trend in time series data. A trend is a long-term increase, decrease, or stationary period in the data. It may be linear or nonlinear. Consider this data from the NASA Global Climate Change website. The points represent the change in global surface temperature relative to 1951-1980 average temperatures. Seventeen of the 18 warmest years in the 136-year record all have occurred since 2001, with the exception of 1998. As you can see, there is a definite upward trend in the data that accelerates somewhere 1980. The Local Trend Model The local trend Kalman filter comes from Ruey S. Tsay's book Analysis of Financial Time Series . ...