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In recent years, there has been a surge of research interest in the analysis of time series and spatial data. While on one hand more and more sophisticated models are being developed, on the other hand the resulting theory and estimation process has become more and more involved. This dissertation addresses the development of statistical inference procedures for data exhibiting dependencies of varied form and structure. In the first work, we consider estimation of the mean squared prediction error (MSPE) of the best linear predictor of (possibly) nonlinear functions of finitely many future observations in a stationary time series. We develop a resampling methodology for estimating the MSPE when the unknown parameters in the best linear predictor are estimated. Further, we propose a bias corrected MSPE estimator based on the bootstrap and establish its second order accuracy. Finite sample properties of the method are investigated through a simulation study. The next work considers nonparametric inference on spatial data. In this work the asymptotic distribution of the Discrete Fourier Transformation (DFT) of spatial data under pure and mixed increasing domain spatial asymptotic structures are studied under both deterministic and stochastic spatial sampling designs. The deterministic design is specified by a scaled version of the integer lattice in IRd while the data-sites under the stochastic spatial design are generated by a sequence of independent random vectors, with a possibly nonuniform density. A detailed account of the asymptotic joint distribution of the DFTs of the spatial data is given which, among other things, highlights the effects of the geometry of the sampling region and the spatial sampling density on the limit distribution. Further, it is shown that in both deterministic and stochastic design cases, for "asymptotically distant" frequencies, the DFTs are asymptotically independent, but this property may be destroyed if the frequencies are "asymptotically close". Some important implications of the main results are also given.

Spelbolag AB has a long history in the Swedish market. Their products are all based on randomness, with a predetermined probability of winning. Some of Spelbolag AB's products are stable in sales throughout the year, while others fluctuate with holidays. Spelbolag AB offers products whose sales are largely influenced by the prize value; higher prize amounts attract more gamblers, while lower prize amounts attract fewer gamblers. Spelbolag AB also has products that are purchased more or less based on the value of the prize, i.e. a higher prize pot increases the number of gamblers and vice versa. Through campaigns, the company wishes to enhance the interest in their products. To estimate the total revenue from the products, a statistical tool has been used. The predictions are made for different key performance indexes (KPIs) which are used as the foundation for some strategic decisions. A wish to improve the statistical tool used by the company has risen due to poor performance. This thesis aimed to create an updated statistical tool. This tool was based on a time series analysis of the weekly net game revenue (NGR). The goal of the time series analysis was to find a statistical model with high forecast accuracy. To find the optimal model for forecast accuracy, a grid search algorithm was used. The performance measure mean squared prediction error (MSPE) was used as a decision base in the grid search along with the mean absolute percentage error (MAPE). Akaike information criterion (AIC) was also estimated as a goodness-of-fit measure. The thesis work resulted in two different SARIMAX models that were analyzed and tested, both including the same exogenous variables. The recommended SARIMAX(1, 0, 2)(1, 1, 1)52 model obtained an MAPE of 4.49%. / Spelbolag AB har en lång historia på den svenska marknaden. Deras produkter är alla slumpmässiga i dess utfall, med en förbestämd chans att vinna. Vissa av Spelbolag ABs produkter har stabil försäljning, medan andra flukturerar med högtider. Spelbolag AB har även produkter vars försäljning påverkas av vinstsumman; fler personer spelar när vinstsumman är hägre och tvärtom. Genom kampanjer önskar företaget öka intresset för sina produkter, och på så vis öka försäljningen. För att prediktera och kunna förutse de totala intäkterna från produkternas försäljning har ett statistisk verktyg använts. Dessa prediktioner har gjorts för olika KPIer, vilka används för att fatta strategiska beslut. Detta verktyg har på den senaste tiden resulterat i dåliga prediktioner, varpå en önskan om att förnya verktyget har uppkommit. Syftet med denna uppsats har därmed varit att uppdatera det statistiska verktyget. Verktyget har baserats på en tidsserieanalys av veckovist netto spelinkomst (NSI). Målet med tidsserieanalysen var att hitta en statistisk modell med hög träffsäkerhet i prediktionerna. För att hitta en optimal modell för just prediktionsnoggrannhet användes algoritmen rutnätssökning. Beslutsunderlaget i denna rutnätssökning var medelkvadratisk predikteringsfel (MSPE) samt medelabsolut procentuellt fel (MAPE). Dessutom estimerades akaike informationskriteriet (AIC) som ett mått på modellanpassning. Uppsatsen resulterade i två olika SARIMAX modeller som båda analyserades och testades, och dessa modeller inkluderade samma exogena variabler. Den rekommenderade SARIMAX(1, 0, 2)(1, 1, 1)52 modellen erhöll ett MAPE av 4.49%.