It sounds like you have more than one regressor and you want them to have different decay factors but still within the Koyck family. If that is the case, here's how to do it. Denote the dependent variable by "S". Let there be 2 regressors, "A" and "…
It is well know that the Koyck model ADL(0,infty) leads to a ARMAX(1,1) model. However when I introduce many more regressors the model becomes very complicated because I am imposing the decay factor lambda onto all extra regressors (and their lags t…
As of Version 18 of PASW Statistics (f.k.a. SPSS Statistics) modules can also be bought 'stand alone'. In this case only PASW Forecasting™ 18 (US price for ESD from the webstore $999.00). See also http://www.spss.com/statistics/
For the packages you listed, EViews is the least expensive, and I might venture a guess that SPSS is the most robust in terms of model autofitting.
SAS: $6K+ first year, $2K+ each additional year (estimates for Base & ETS)
SPSS: $2,798 (Base & Fore…
First I’d say to try JMulTi. It’s free and easy to use, so if it can accomplish what you want to accomplish...
As far as commercial software: Stata, Stata, and then maybe Stata.
MCMC stands for Markov Chain Monte Carlo.
Metropolis Hastings is in the class of MCMC algorithms. Its used to maximize a likelihood and find estimates of parameters. There is an initial point and a random jumping function...ie jump to a nearby point in parameter space using a random pick from a multi-normal distribution. Then compute the likelihood at the new point. If you have gone up hill and increased the likelihood then keep the new point. If you have gone down hill, draw a random number U, and keep the new point anyway if U meets some given criteria. So all of the uphill points are kept and some of the downhill points are accepted randomly. Then repeat this process thousands of times. Record each accepted point on the likelihood surface. After a while referred to as 'burn-in' you should have arrived in the neighborhood of the maximum likelihood. If shown on the map it will look like a cloud of points all around the peak of the mountain. Throw away the first half of the accepted points. Test the Markov Chain for convergence. Then take percentiles to describe the location in each dimension(parameter). Thats one chain. Start another chain at a different initial point to make sure that it arrives at the same maximum. Likelihoods can sometimes be as compicated as the mountain in the slide with ridges, secondary maximums etc. The Monte Carlo part of MCMC is the random jumping and random acceptance of downhill points.
In one or two dimensions MCMC is not as efficient as other methods for maximization. When dimensions get higher it become faster and more efficient. For that particular data set I had six dimensions and a large data set. It was challenging the limits of my little lap top. So speed and effieicency were important to me. Intuitively MCMC is just random sampling the likelihood surface around the peak.