The objectives of this thesis are the time series forecasting of tornadoes in Oklahoma, estimating property damage due to tornadoes in the United States using multivariate data mining models, and generating inferences from past tornado events in the United States though data mining. Firstly, univariate time series modeling is applied to generate monthly forecasts for the estimated property damage due to the tornado event, the length of the tornado, the width of the tornado, and the tornado strike location, which is determined by the beginning latitude and beginning longitude of the tornado event. Naïve forecasts, seasonal naïve forecasts, trailing moving average, the Holt-Winters model, exponential smoothing, linear regression, ARIMA, and artificial neural networks are the time series models investigated in this research. In each case, after training and validating different time series models, the best performing model is selected to generate monthly forecasts with prediction intervals from January 2015 to December 2015. After comparing the monthly forecasts with the true values for the year 2015, it is observed that the true values lie within the forecasted prediction intervals for each time series on all occasions. Secondly, data mining models, namely multiple linear regression, ridge regression, the lasso, principal components regression, partial least squares regression, generalized additive models (GAMs), decision trees, bagging, random forests and boosting are applied to the dataset of 64519 tornado events over a time period of 66 years within the United States, with the property damage as the response variable, and other features as independent variables. The primary goal is estimation and the secondary goal is inference. After the training and 10-fold cross validation of different data mining models, boosting is found to generate the most accurate estimates for property damage. The results of inference from the lasso indicate that the property damage increases by $53819 for every 0.1 mile increase in the tornado length, and by $9780 for every 1 foot increase in tornado width.

Multivariate time series forecasting(MLTS) has been a mainstream tool for forecasting in economics, traffic modelling, economics, future shipments, temperature forecasts(temperature forecast solely on previous year data(as shown in "Lugano temperature forecast", it requires weather modelling too). The basic assumption in multivariate time series forecasting is that different variables are dependent on each other, but existing methods are not very efficient at finding a good neighbourhood relationship. It can be said that they fail at fully exploiting the spatial dependencies between the multiple features of a time series. Change in a single variable directly or indirectly leads to change in the other variables, for eg. change in temperature would directly effect the electricity consumption of a given area It can indirectly affect the stock price of a certain company. Using MLTS we can capture the trends and overall changes seen with dynamically changes variables. In this work we conduct a study between Graph Neural networks with (Ridge and Lasso) Regression to understand the kind of results we obtain from Machine learning models and classical statistical method. In the present methods based on statistics, such as Gaussian process models and auto regressive models assume linear dependency among variables.

This is a model selection coding script for predicting time series covering comparison between Lasso, PM and kitchen sink model as well as based on both MSE and economic loss function. The data is downloaded from Amit Goyal’s web site and is an extended version of the data used by Goyal and Welch (Review of Financial Studies, 2008). It contains monthly information on US stock returns as well as on a range of predictor variables proposed in the literature.