MSc (Statistics) / Department of Statistics / Over the years researchers have been modeling inflation rate in Ghana using linear models such as Autoregressive Integrated Moving Average (ARIMA), Autoregressive Moving Average (ARMA) and Moving Average (MA). Empirical research however, has shown that financial data, such as inflation rate, does not follow linear patterns. This study seeks to model and forecast inflation in Ghana using nonlinear models and to establish the existence of nonlinear patterns in the monthly rates of inflation between the period January 1981 to August 2016 as obtained from Ghana Statistical Service. Nonlinearity tests were conducted using Keenan and Tsay tests, and based on the results, we rejected the null hypothesis of linearity of monthly rates of inflation. The Augmented Dickey-Fuller (ADF) was performed to test for the presence of stationarity. The test rejected the null Hypothesis of unit root at 5% significant level, and hence we can conclude that the rate of inflation was stationary over the period under consideration. The data were transformed by taking the logarithms to follow nornal distribution, which is a desirable characteristic feature in most time series. Monthly rates of inflation were modeled using threshold models and their fitness and forecasting performance were compared with Autoregressive (AR ) models. Two Threshold models: Self-Exciting Threshold Autoregressive (SETAR) and Logistic Smooth Threshold Autoregressive (LSTAR) models, and two linear models: AR(1) and AR(2), were employed and fitted to the data. The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) were used to assess each of the fitted models such that the model with the minimum value of AIC and BIC, was judged the best model. Additionally, the fitted models were compared according to their forecasting performance using a criterion called mean absolute percentage error (MAPE). The model with the minimum MAPE emerged as the best forecast model and then the model was used to forecast monthly inflation rates for the year 2017. The rationale for choosing this type of model is contingent on the behaviour of the time-series data. Also with the history of inflation modeling and forecasting, nonlinear models have proven to perform better than linear models. The study found that the SETAR and LSTAR models fit the data best. The simple AR models however, out-performed the nonlinear models in terms of forecasting. Lastly, looking at the upward trend of the out-sample forecasts, it can be predicted that Ghana would experience double digit inflation in 2017. This would have several impacts on many aspects of the economy and could erode the economic gains i made in the year 2016. Our study has important policy implications for the Central Bank of Ghana which can use the data to put in place coherent monetary and fiscal policies that would put the anticipated increase in inflation under control.

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Anomaly detection on time series forecasts can be used by many industries in especially forewarning systems that can predict anomalies before they happen. Infor (Sweden) AB is software company that provides Enterprise Resource Planning cloud solutions. Infor is interested in predicting anomalies in their data and that is the motivation for this thesis work. The general idea is firstly to forecast the time series and then secondly detect and classify anomalies on the forecast. The first part is time series forecasting and the second part is anomaly detection and classification done on the forecasted values. In this thesis work, the time series forecasting to predict anomalous behaviour is done using two strategies namely the recursive strategy and the direct strategy. The recursive strategy includes two methods; AutoRegressive Integrated Moving Average and Neural Network AutoRegression. The direct strategy is done with ForecastML-eXtreme Gradient Boosting. Then the three methods are compared concerning performance of forecasting. The anomaly detection and classification is done by setting a decision rule based on a threshold. In this thesis work, since the true anomaly thresholds were not previously known, an arbitrary initial anomaly threshold is set by using a combination of statistical methods for outlier detection and then human judgement by the company commissioners. These statistical methods include Seasonal and Trend decomposition using Loess + InterQuartile Range, Twitter + InterQuartile Range and Twitter + GESD (Generalized Extreme Studentized Deviate). After defining what an anomaly threshold is in the usage context of Infor (Sweden) AB, then a decision rule is set and used to classify anomalies in time series forecasts. The results from comparing the classifications of the forecasts from the three time series forecasting methods are unfortunate and no recommendation is made concerning what model or algorithm to be used by Infor (Sweden) AB. However, the thesis work concludes by recommending other methods that can be tried in future research.

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There is no single commonly adapted model that explains the influence that various monetary policy instruments carry for the economy. During 2011-2017, the Swedish inflation rate has remained below the 2 percent target which has led the Riksbank to take measures aimed at stimulating the inflation. As of May 2018, the repo rate has experienced a number of decreases and is now at 􀀀0:50% which represents an unprecedentedly low level. With the inflation rate remaining below the target whilst the housing market has experienced substantial growth and recent decline, the question arises regarding what impact the repo rate exerts on various macroeconomic measures. In this paper, a statistical time series analysis is conducted using a Vector Autoregression model and the impulse responses are studied. A model of 7 economic variables is constructed to specially study the effect of the repo rate on employment and housing prices. Results demonstrate that rational expectations exist in the economy. Furthermore, results show that the repo rate influences factors affected by inflation rapidly, exerting maximum influence during the first year after the shock. On the other hand, real variables based on quantitative measures that are adjusted for inflation experience the greatest influence of the repo rate after a delay of 6 to 7 quarters. Employment experiences the greatest negative response to a repo rate shock after 7 quarters, with a magnitude of 0.317 standard deviations per standard deviation in the repo rate shock. Housing prices experience the greatest negative response to a repo rate shock after 4 quarters, with a magnitude of 0.209 standard deviations per standard deviation in the repo rate shock. / Det finns ingen allmänt vedertagen modell som beskriver olika penningpolitiska instruments påverkan på ekonomin. Under 2011-2017 har Sveriges inflationstakt legat under 2-procentsmålet vilket har fått Riksbanken att vidta åtgärder i syfte att stimulera inflationen. Fram till maj 2018 har upprepade sänkningar av reporäntan genomförts och den ligger i dagsläget på 0:50% vilket är den lägsta nivån någonsin. Då inflationstakten inte nått målet samtidigt som bostadsmarknaden har upplevt kraftig tillväxt och nylig nedgång uppstår frågan gällande vilken effekt som reporäntan utlovar på diverse makroekonomiska mått. I denna rapport genomförs en statistisk tidsserieanalys med en vektorautoregression och impuls-responserna studeras. En modell med 7 ekonomiska variabler skapas för att specifikt studera effekten av reporäntan på sysselsättning och bostadspriser. Resultaten visar att rationella förväntningar finns i ekonomin. Vidare visar resultaten att reporäntan influerar inflationspåverkade variabler omgående, med maximal påverkan inom det första året efter chocken. Å andra sidan påverkas volymbaserade variabler som justeras för inflation maximalt först efter en fördröjning på 6 till 7 kvartal. Sysselsättningen upplever störst negativ påverkan från en reporäntechock efter 7 kvartal motsvarande 0.317 standardavvikelser per standardavvikelse i chocken. Bostadspriser upplever störst negativ påverkan från en reporäntechock efter 4 kvartal motsvarande 0.209 standardavvikelser per standardavvikelse i chocken.

Die derzeitige Wiederkehr von protektionistischen Maßnahmen und Illiberalismus erfordert ein detaillierteres Verständnis der Wechselwirkungen zwischen wirtschaftlichen und politischen Faktoren. Die vorliegende Doktorarbeit besteht aus vier Artikeln, die unser Verständnis der komplexen Wechselwirkungen zwischen Handel, Demokratie, Entwicklung und Konflikt voranbringen. Der erste Artikel (Boese 2015) fragt: Führen Revolutionen zu mehr Demokratie? Die untersuchten revolutionären Konflikte sind positiv mit dem demokratischen Weg eines Landes verbunden. Darüber hinaus führt der Artikel ein neues Maß für Demokratie ein, den (X-) Pol-Index. Der zweite Artikel (Boese 2019) vergleicht die Demokratiemaße von PolityIV, Freedom House und V-Dem. V-Dem Maße übertreffen die anderen in allen Bereichen. Der Artikel bietet eine Einführung in die Demokratiemessung, einen Vergleich der Vor- und Nachteile jedes Maßes in empirischen Analysen und Fallstudien, um die Unterschiede zwischen den Indizes zu veranschaulichen. Der dritte Artikel (Boese & Kamin 2019) untersucht das Problem inkonsistenter Länderkodierungen zwischen verschiedenen Makrodatensätzen. Es führt zu einer Verzerrung der Stichprobenauswahl, da sich in Konfliktländern oft Name und Grenzen des Staates ändern. Dadurch wird die Zuverlässigkeit von Schlussfolgerungen aus statistischen Analysen, insbesondere in der Konfliktökonomie, eingeschränkt. Detaillierte Übersichtstabellen der Länderkodierungsdifferenzen werden bereitgestellt. Der vierte Artikel (mit K. Kamin, CAU Kiel) untersucht die Wechselwirkungen von Demokratie, Entwicklung, Handel und Konflikt. In einem länderspezifischen VAR werden die Auswirkungen von Schocks auf einen der vier Faktoren untersucht. Die Ergebnisse zeigen, dass diese Effekte im Laufe der Zeit in und innerhalb von Ländern sehr heterogen sind. Der Artikel erhielt den Michael D. Intrilligator Best PhD Student Paper Award auf der 23. International Conference on Economics and Security in Madrid (Juni 2019). / The current return to protectionist measures coinciding with a rise of illiberalism triggers the need for a more detailed understanding of the interactions of economic and political dimensions. This thesis consists of four articles advancing our understanding of the complex interactions between trade, democracy, development and conflict. The first article (Boese 2015) asks: do revolutions lead to more democracy? The revolutionary conflicts examined are positively associated with a country's democratic path. In addition, the article introduces a new measure of democracy, the (X-)Pol Index. The second article (Boese 2019) compares measure validity and reliability of Polity2, Freedom House and V-Dem democracy indices. The latter surpass the former in all relevant areas. The article provides an introduction to democracy measurement, a comparison of the advantages and disadvantages of each measure in empirical analyses and several case studies to illustrate differences across the three indices. The third article (Boese & Kamin 2019) shows that in spite of standardization efforts the problem of inconsistent country coding across and within disciplines persists. This leads to sample selection bias as countries in conflict often undergo state name and border changes. In turn, reliability of inferences drawn from statistical analysis, in particular in conflict and peace economics, is limited. Detailed overview tables of the gravest country coding discrepancies are provided. The fourth article (with K. Kamin, CAU Kiel) examines the interactions of democracy, development, trade and conflict. It employs a country-specific VAR to study the effects of shocks in any of the four factors on one another. Results show that these effects are vastly heterogenous across and within countries over time. The article received the Michael D. Intrilligator Best PhD Student Paper Award at the 23rd International Conference on Economics and Security in Madrid, Spain (June 2019).

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With advanced technology and information explosion, the data of interest often have complex structures, with the large size and dimensions in the form of continuous or discrete features. There is an emerging need for data reduction, efficient modeling, and model inference. For example, data can contain millions of observations with thousands of features. Traditional methods, such as linear regression or LASSO regression, cannot effectively deal with such a large dataset directly. This dissertation aims to develop several techniques to effectively analyze large datasets with complex structures in the observational, experimental and time series data. In Chapter 2, I focus on the data reduction for model estimation of sparse regression. The commonly-used subdata selection method often considers sampling or feature screening. Un- der the case of data with both large number of observation and predictors, we proposed a filtering approach for model estimation (FAME) to reduce both the size of data points and features. The proposed algorithm can be easily extended for data with discrete response or discrete predictors. Through simulations and case studies, the proposed method provides a good performance for parameter estimation with efficient computation. In Chapter 3, I focus on modeling the experimental data with quantitative-sequence (QS) factor. Here the QS factor concerns both quantities and sequence orders of several compo- nents in the experiment. Existing methods usually can only focus on the sequence orders or quantities of the multiple components. To fill this gap, we propose a QS transformation to transform the QS factor to a generalized permutation matrix, and consequently develop a simple Gaussian process approach to model the experimental data with QS factors. In Chapter 4, I focus on forecasting multivariate time series data by leveraging the au- toregression and clustering. Existing time series forecasting method treat each series data independently and ignore their inherent correlation. To fill this gap, I proposed a clustering based on autoregression and control the sparsity of the transition matrix estimation by adap- tive lasso and clustering coefficient. The clustering-based cross prediction can outperforms the conventional time series forecasting methods. Moreover, the the clustering result can also enhance the forecasting accuracy of other forecasting methods. The proposed method can be applied on practical data, such as stock forecasting, topic trend detection. / Doctor of Philosophy / This dissertation focuses on three projects that are related to data reduction and statistical modeling of data with complex structures. In chapter 2, we propose a filtering approach of data for parameter estimation of sparse regression. Given data with thousands of ob- servations and predictors or even more, large storage and computation spaces is need to handle these data. It is challenging to computational power and takes long time in terms of computational cost. So we come up with an algorithm (FAME) that can reduce both the number of observations and predictors. After data reduction, this subdata selected by FAME keeps most information of the original dataset in terms of parameter estimation. Compare with existing methods, the dimension of the subdata generated by the proposed algorithm is smaller while the computational time does not increase. In chapter 3, we use quantitative-sequence (QS) factor to describe experimental data. One simple example of experimental data is milk tea. Adding 1 cup of milk first or adding 2 cup of tea first will influence the flavor. And this case can be extended to cases when there are thousands of ingredients need to be input into the experiment. Then the order and amount of ingredients will generate different experimental results. We use QS factor to describe this kind of order and amount. Then by transforming the QS factor to a matrix containing continuous value and set this matrix as input, we model the experimental results with a simple Gaussian process. In chapter 4, we propose an autoregression-based clustering and forecasting method of multi- variate time series data. Existing research works often treat each time series independently. Our approach incorporates the inherent correlation of data and cluster related series into one group. The forecasting is built based on each cluster and data within one cluster can cross predict each other. One application of this method is on topic trending detection. With thousands of topics, it is unfeasible to apply one model for forecasting all time series. Considering the similarity of trends among related topics, the proposed method can cluster topics based on their similarity, and then perform forecasting in autoregression model based on historical data within each cluster.

不動產價格的影響因素可按影響範圍區分為三大類，分別為影響整體不動產市場的「總體環境因素」，對一定範圍內不動產產生價格影響的「區域環境因素」，及對於單一不動產價格有所影響的「房屋個體因素」。其中，區域環境因素為影響個別不動產價格之首要因素，不動產之價格會受到所屬區域之政治、經濟、自然、社會等因素影響，「公共建設因素」為重要之區域環境之一，包含公共設施水準及其配置狀態。影響個別不動產價格之次要因素為「房屋個體因素」，可再次細分為三大影響因素如下：房屋本身所具有的特徵因素，即建築物之內部結構；房屋的建築方式，住宅類型等與全棟房屋有關的因素；與房屋鄰近地區環境有關的因素。而集合式與獨立式住宅因分屬不同房屋類型，即上述房屋價格形成因素中「房屋之建築方式」。實際交易上，獨立式住宅多半以「整棟建物」作為交易計算單位，對於坐落之基地權利持分通常為全部，而集合式住宅係以「樓層」、「戶」作為交易之計算單位，所有之基地持分與其他住戶共同持有，基於上述差異，過去研究多將建築方式視為影響房屋價格的條件之一，並據此分類次市場，因此較少有研究同時探討二者在空間分布上所具有的區位差異，及購屋者對於環境的偏好是否有所不同。且過去文獻多半以使用傳統迴歸模型為主要分析方法。但傳統迴歸分析所使用最小平方法迴歸模型，經常會產生殘差項存在有空間自相關的問題，及空間本身所存在之空間異質性偏誤，即空間不穩定性。因此 本文以台中市都會區內之住家使用房屋為樣本，依特徵價格理論將獨立式住宅與集合式住宅視為差異化商品，其內外特徵納入變數，使用GeoDa軟體進行空間自相關分析，並使用ArcGIS軟體中的地理加權迴歸模組（GWR）進行迴歸分析，藉以探討不同類型房屋所偏好之外部特徵，瞭解不同空間環境對房屋價格之影響及台中市都會區空間發展型態，並驗證其於規劃建設產生的空間不穩定性。 研究結果顯示，台中市建立之重大市政建設及土地開發計畫會影響集合式住宅與獨立式住宅之地價熱點分布，其共同之房價熱點均座落於高地價市地重劃區及重大市政建設分布位置，而獨立式住宅之房價熱點，進一步分布於與高地價市重劃區鄰近之市地重劃區；在購屋者對周圍設施偏好方面，集合式住宅購屋者對於國中小學、大學、重大市政建設、市場、公園均有顯著偏好，惟獨立式住宅購屋者對於大學、重大市政建設、公園有顯著偏好，對於國中小學、市場有不偏好情形，顯示不同類型住宅對於公共設施之偏好不完全相同；集合式住宅與獨立式住宅之房屋特徵屬性呈現空間不穩定性，分析結果顯示，上述二種住宅類型，對於本研究所有公共設施距離特徵屬性均呈現空間不穩定、非均質性的結果，顯示不同類型住宅均會與彼此具有相依性，並形成各區域間的異質性。 / Locational characteristics are the determinants of house prices. While former research have examined the effects of proximity to resources and facilities have on residential property values, and the change of the importance as located regions or submarkets vary, the effects of different types of houses are rarely compared due to their dissimilarity in ways of building and ownership. Do house price effects of the same facility alter when properties are situated in different submarkets? Further, the issues of spatial non-stationarity are usually overlooked by previous studies. By using transaction data of two common types of residential houses in Taichung City, we found house price hot spots of both detached houses and condos in regions with major constructions and development plans. Apart from the mutual hot spots found in high land price redevelopment zones, we also discovery hot spots of detached houses in areas in proximity to these redevelopment zones. As for desirable facilities for home buyers, neighborhood schools, universities, major constructions, local markets and parks were found to have an notable price impact on condos, whereas only universities, major constructions and parks in vicinity of in detached houses can we found significant price effects, suggesting the differences in the preference of consumers in distinct regions. Also, spatial dependence and heterogeneity are verified in both types of houses, making the entire market area spatial non-stationary.

Following the debate by empirical finance research on the presence of non-linear predictability in stock market returns, this study examines forecasting abilities of nonlinear STAR-type models. A non-linear model methodology is applied to daily returns of FTSE, S&P, DAX and Nikkei indices. The research is then extended to long-horizon forecastability of the four series including monthly returns and a buy-and-sell strategy for a three, six and twelve month holding period using non-linear error-correction framework. The recursive out-of-sample forecast is performed using the present value model equilibrium methodology, whereby stock returns are forecasted using macroeconomic variables, in particular the dividend yield and price-earnings ratio. The forecasting exercise revealed the presence of non-linear predictability for all data periods considered, and confirmed an improvement of predictability for long-horizon data. Finally, the present value model approach is applied to the housing market, whereby the house price returns are forecasted using a price-earnings ratio as a measure of fundamental levels of prices. Findings revealed that the UK housing market appears to be characterised with asymmetric non-linear dynamics, and a clear preference for the asymmetric ESTAR model in terms of forecasting accuracy.