1. Data evaluation. Analyse completeness of data. Are there missed data (besides weekends)? How many missed data points are in your time series? Are the dates of missed values the same for your time series? What may be the reasons for missing? (10 marks) 2. Preprocessing. How can you handle the missed values in your data (explain at least three approaches)? Use the simple rule: fill in a missed value by the closest in time past existing value. Plot the results. Transform the time series to the dimensionless log-returns: yi=ln(xi/xi-1). Calculate the variance and the mean. Normalise to the z-score (zero mean and unit standard deviation). Plot the results. (15 marks) 3. Segmentation. Prepare the bottom-up piecewise linear segmentation for the transformed and normalised log-return time series. Use the following MSE tolerance levels: 0.04, 0.1, 0.25 (the thresholds of the mean square errors). Plot the results. Are the segment similar for different time series you analysed? (25 marks) 4. Prediction (linear regression). Chose one of the transformed and normalised log-return time series as a target () and other 3 as supporting data 1 (), 2 (), 3 (), where = 1, ... , . Evaluate ( + 1) (the next day value of () as a linear function of (), 1 (), 2 (), 3 (): ( + 1) = ((), 1 (), 2 (), 3 ()) Provide scatter diagrams of (g(t),g(t+1)). Provide plots of (), (), the residual and the scatter diagrams. Compare your result of forecasting to the next-day forecast ( + 1) = (). (How will you measure the quality of forecasting and compare these results?) (25 marks) 5. Prediction (Adaline). Use an adaptive summator (that is, Adaline or delta-rule) for creation online predictor of ( + 1) from the previous task. (Adaline receives at each step t values of inputs (), 1 (), 2 (), 3 (), a value of the output, finds the error and corrects the weights by the deltarule). Try different learning rates (correction steps). Select the best. How do you optimize the learning rate? Present the plots of square error as function of time. (25 marks)