Inflation is one of the most important macroeconomic variables. It is vital that policy makers receive accurate forecasts of inflation so that they can adjust their monetary policy to attain stability in the economy which has been shown to lead to economic growth. The purpose of this study is to model inflation and evaluate if applying the Kalman filter to SARIMA models lead to higher forecast accuracy compared to just using the SARIMA model. The Box-Jenkins approach to SARIMA modelling is used to obtain well-fitted SARIMA models and then to use a subset of observations to estimate a SARIMA model on which the Kalman filter is applied for the rest of the observations. These models are identified and then estimated with the use of monthly inflation for Luxembourg, Mexico, Portugal and Switzerland with the target to use them for forecasting. The accuracy of the forecasts are then evaluated with the error measures mean squared error (MSE), mean average deviation (MAD), mean average percentage error (MAPE) and the statistic Theil's U. For all countries these measures indicate that the Kalman filtered model yield more accurate forecasts. The significance of these differences are then evaluated with the Diebold-Mariano test for which only the difference in forecast accuracy of Swiss inflation is proven significant. Thus, applying the Kalman filter to SARIMA models with the target to obtain forecasts of monthly inflation seem to lead to higher or at least not lower predictive accuracy for the monthly inflation of these countries.

This paper examines the forecast accuracy of an unrestricted Vector Autoregressive (VAR) model for GDP, relative to a comparable Vector Error Correction (VEC) model that recognizes that the data is characterized by co-integration. In addition, an alternative forecast method, Intercept Correction (IC), is considered for further comparison. Recursive out-of-sample forecasts are generated for both models and forecast techniques. The generated forecasts for each model are objectively evaluated by a selection of evaluation measures and equal accuracy tests. The result shows that the VEC models consistently outperform the VAR models. Further, IC enhances the forecast accuracy when applied to the VEC model, while there is no such indication when applied to the VAR model. For certain forecast horizons there is a significant difference in forecast ability between the VEC IC model compared to the VAR model.

This study is a comparison of forecasting methods for predicting the daily maximum air temperatures in Uppsala using real data from the Swedish Meteorological and Hydrological Institute. The methods for comparison are univariate time series approaches suitable for the data and represent both standard and more recently developed methods. Specifically, three methods are included in the thesis: neural network, ARIMA, and naïve. The dataset is split into a training set and a pseudo out of sample test set. The assessment of which method best forecast the daily temperature in Uppsala is done by comparing the accuracy of the models when doing walk forward validation on the test set. Results show that the neural network is most accurate for the used dataset for both one-step and all multi-step forecasts. Further, the only same-step forecasts from different models that have a statically significant difference are from the neural network and naïve for one- and two-step forecasts, in favor of the neural network.

<p>This doctoral thesis is comprised of four papers that all relate to the subject of Time Series Analysis.</p><p>The first paper of the thesis considers point estimation in a nonnegative, hence non-Gaussian, AR(1) model. The parameter estimation is carried out using a type of extreme value estimators (EVEs). A novel estimation method based on the EVEs is presented. The theoretical analysis is complemented with Monte Carlo simulation results and the paper is concluded by an empirical example.</p><p>The second paper extends the model of the first paper of the thesis and considers semiparametric, robust point estimation in a nonlinear nonnegative autoregression. The nonnegative AR(1) model of the first paper is extended in three important ways: First, we allow the errors to be serially correlated. Second, we allow for heteroskedasticity of unknown form. Third, we allow for a multi-variable mapping of previous observations. Once more, the EVEs used for parameter estimation are shown to be strongly consistent under very general conditions. The theoretical analysis is complemented with extensive Monte Carlo simulation studies that illustrate the asymptotic theory and indicate reasonable small sample properties of the proposed estimators.</p><p>In the third paper we construct a simple nonnegative time series model for realized volatility, use the results of the second paper to estimate the proposed model on S&P 500 monthly realized volatilities, and then use the estimated model to make one-month-ahead forecasts. The out-of-sample performance of the proposed model is evaluated against a number of standard models. Various tests and accuracy measures are utilized to evaluate the forecast performances. It is found that forecasts from the nonnegative model perform exceptionally well under the mean absolute error and the mean absolute percentage error forecast accuracy measures.</p><p>In the fourth and last paper of the thesis we construct a multivariate extension of the popular Diebold-Mariano test. Under the null hypothesis of equal predictive accuracy of three or more forecasting models, the proposed test statistic has an asymptotic Chi-squared distribution. To explore whether the behavior of the test in moderate-sized samples can be improved, we also provide a finite-sample correction. A small-scale Monte Carlo study indicates that the proposed test has reasonable size properties in large samples and that it benefits noticeably from the finite-sample correction, even in quite large samples. The paper is concluded by an empirical example that illustrates the practical use of the two tests.</p>

This doctoral thesis is comprised of four papers that all relate to the subject of Time Series Analysis. The first paper of the thesis considers point estimation in a nonnegative, hence non-Gaussian, AR(1) model. The parameter estimation is carried out using a type of extreme value estimators (EVEs). A novel estimation method based on the EVEs is presented. The theoretical analysis is complemented with Monte Carlo simulation results and the paper is concluded by an empirical example. The second paper extends the model of the first paper of the thesis and considers semiparametric, robust point estimation in a nonlinear nonnegative autoregression. The nonnegative AR(1) model of the first paper is extended in three important ways: First, we allow the errors to be serially correlated. Second, we allow for heteroskedasticity of unknown form. Third, we allow for a multi-variable mapping of previous observations. Once more, the EVEs used for parameter estimation are shown to be strongly consistent under very general conditions. The theoretical analysis is complemented with extensive Monte Carlo simulation studies that illustrate the asymptotic theory and indicate reasonable small sample properties of the proposed estimators. In the third paper we construct a simple nonnegative time series model for realized volatility, use the results of the second paper to estimate the proposed model on S&amp;P 500 monthly realized volatilities, and then use the estimated model to make one-month-ahead forecasts. The out-of-sample performance of the proposed model is evaluated against a number of standard models. Various tests and accuracy measures are utilized to evaluate the forecast performances. It is found that forecasts from the nonnegative model perform exceptionally well under the mean absolute error and the mean absolute percentage error forecast accuracy measures. In the fourth and last paper of the thesis we construct a multivariate extension of the popular Diebold-Mariano test. Under the null hypothesis of equal predictive accuracy of three or more forecasting models, the proposed test statistic has an asymptotic Chi-squared distribution. To explore whether the behavior of the test in moderate-sized samples can be improved, we also provide a finite-sample correction. A small-scale Monte Carlo study indicates that the proposed test has reasonable size properties in large samples and that it benefits noticeably from the finite-sample correction, even in quite large samples. The paper is concluded by an empirical example that illustrates the practical use of the two tests.