"Those who have knowledge, don't predict. Those who predict, don't have knowledge. "              --Lao Tzu

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LINEAR PREDICTION                                                                                                    predict.pdf

Estimation of variables given some related variables is a very important problem. Many times one needs to estimate the values of Random Variables given some information about related variables. e.g. given the temperature at India Gate in Delhi, what is the estimate of the temperature at Rashtrapati Bhawan? or given that the stock market behaved in a certain way this week, what can be predicted about its behaviour tommorow? Questions like these lead us into the theory of estimation and prediction.

Estimation or prediction is one the of the most celebrated problems in Time Series Analysis. The idea is that given a sequence, what can you say about the value of the next sample? Such things are used extensively in Signal Processing and Coding theory for compression of data (i.e. given a sequence of symbols, can you predict the next one so that you don't need to store it and hence increase the rate of compression). Linear Prediction Coding is a important class of algorithms in areas like Speech Processing etc.

So, if the estimated value of the next sample (or variable to be estimated) is a linear function of the past samples (or available infromation), the term Linear Prediction is used. One can also do Non-Linear Prediction but then things get mathematically complicated.

I tried simulating two standard Linear Prediction algorithms: Levinson-Durbin Recursion and Weighted Least Squares Error Algorithm using MATLAB and was really surprised to see the results. I experimented with images and it is almost impossible to see the difference between the actual images and the predicted outputs. Here is the report: predict.pdf