<p>I denna uppsats undersöks om befintliga konsumtionsmodeller förbättras när det adderas en specifik variabel för framtidsförväntningar till dem eller om framtidsförväntningarna redan är inbakade i dessa modeller genom andra variabler. För att undersöka detta har en variabel för hushållens förväntningar adderats till två befintliga konsumtionsmodeller. Därefter har skillnaderna jämförs, dels i förklarningsvärde och dels i prognosförmåga. Undersökning baseras på svensk data från tidsperioden 1980 till 2006. Resultaten tyder på att hushållens förväntningar är icke-signifikanta i modellskattningarna. Den första modellen får dock signifikant bättre prognosförmåga då variabeln för framtidsförväntningar inkluderats.</p>

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I denna uppsats undersöks om befintliga konsumtionsmodeller förbättras när det adderas en specifik variabel för framtidsförväntningar till dem eller om framtidsförväntningarna redan är inbakade i dessa modeller genom andra variabler. För att undersöka detta har en variabel för hushållens förväntningar adderats till två befintliga konsumtionsmodeller. Därefter har skillnaderna jämförs, dels i förklarningsvärde och dels i prognosförmåga. Undersökning baseras på svensk data från tidsperioden 1980 till 2006. Resultaten tyder på att hushållens förväntningar är icke-signifikanta i modellskattningarna. Den första modellen får dock signifikant bättre prognosförmåga då variabeln för framtidsförväntningar inkluderats.

Global climate models (GCM) have been used for nearly two decades now as a tool to investigate and analyze past, present, and future weather and climate. Even though the first several generations of climate models were very simple, today's models are very sophisticated. They use complex parameterization schemes to approximate many nonlinear physical fields. In these models, the resolution and time steps can be set to be as small or as large as desired. In either case, the model generates over 100 atmospheric variables and 20 land surface variables that can be reported daily or monthly. The Community Atmospheric Model Version Two global climate model spends over sixty percent of the time computing shortwave and longwave parameterization schemes. Our goal is to replace its shortwave scheme with empirical methods and show that accuracy of the tropospheric variables is not compromised when using these empirical methods. We found that an autoregressive moving average (ARMA) model can be used to simulate the solar radiation at the top of the model atmosphere. However, the calculated insolation value is only valid for one particular grid point. To simulate the radiation over the entire globe, many ARMA models need to be determined. We also found that large 4-10-10-1 neural networks can be used to simulate the solar radiation to within 2 W m-2. However, much smaller and manageable neural networks can be used to simulate the complete solar insolation term if the neural network only simulates the residual after the annual and diurnal cycles and removed from the field (referred to as the - method). By using the neural network in the - method and by setting the eccentricity term to a constant, we were able to cut the models processing of the solar insolation by at least a factor of four.

Most recorded data are rounded to the nearest decimal place due to the precision of the recording mechanism. This rounding entails errors in estimation and measurement. In this paper, we compare the performances of three types of estimators based on rounded data from time series models, namely A-K corrected estimator, approximate MLE and the SOS estimator. In order to perform the comparison, the A-K corrected estimators for the MA(1) model are derived theoretically. To improve the efficiency of the estimation, two types of variance-reduction estimators are further proposed, which are based on linear combinations of aforementioned three estimators. Simulation results show the proposed variance reduction estimators significantly improve the estimation efficiency.

Recently, there are more and more literatures discuss on the issues of investment strategies of leveraged ETFs. In our works, we concentrate our issues on optimal leverage of ETF of S&P 500 index. Based on ARMA-GARCH model¡¦s assumption, we find out that the forecasting optimal leverage can be shown in a formula which contains return and characteristic function. In this paper, we use MA(1)-GARCH(1,1) to forecast volatility based on 1008 rolling window to forecast one day ahead¡¦s volatility; and our estimation time is start from 1954 to March 2011. In this paper, we present four dynamic leverage models (Normal, Student T, VG, and Best model¡¦s leverage) to find out the payoffs under these models. In our model, the forecasting accuracy is just about 55% which is slightly higher than SPX raise probability. But during long-term compound effect, the dynamic leverage models can out-perform than constant leverage. There may exist some important factors in these results, one of them is the crash forecasting ability. During 1980 to 2011 SPX has 14 big crashes and these models can effectively avoid 10 big crashes. In short-term investment horizon none of these five models are always outperform than others but in long-term investment horizon the strategy of best model¡¦s leverage can always earn money when investment horizon is 2400 days.

While the much more use of leverage could be effective in generating alpha o investment, the Kelly strategy is an attractive approach to capital creation and growth. It is originated from the Kelly criterion dubbed ¡§ fortunes formula ¡§ which maximizes the long run growth rate of wealth. There is a tradeoff of rate of return versus risk/volatility as a asymptotic function solution of leverage or position size determined by the application of EGARCH model in the different residual assumptions given by the Normal, Generalized Hyperbolic, and the Generalized Error distributions. No matter there is any timing ability in any strategy, risk management is much more important especially with many repeated trading. We present the performance and risk control of the leveraged ETFs tracked the S&P 500 index in the past ten years using optimal leverage strategy derived by the full Kelly and fraction Kelly criterion.

Most of the time series are constructed by some kind of aggregation and temporal aggregation that can be defined as aggregation over consecutive time periods. Temporal aggregation takes an important role in time series analysis since the choice of time unit clearly influences the type of model and forecast results. A totally different time series model can be fitted on the same variable over different time periods. In this thesis, the effect of temporal aggregation on univariate time series models is studied by considering modeling and forecasting procedure via a simulation study and an application based on a southern oscillation data set. Simulation study shows how the model, mean square forecast error and estimated parameters change when temporally aggregated data is used for different orders of aggregation and sample sizes. Furthermore, the effect of temporal aggregation is also demonstrated through southern oscillation data set for different orders of aggregation. It is observed that the effect of temporal aggregation should be taken into account for data analysis since temporal aggregation can give rise to misleading results and inferences.

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Att i förväg försöka förutsäga vilket lag som kommer vinna i en fotbollsmatch har nog de flesta försökt sig på någon gång. Att gissa och att faktiskt försöka att analysera båda lagens förutsättningar är två väldigt olika metoder att komma fram till sitt resultat. I och med att datorkraften de senaste åren kraftigt förbättrats har det också kommit fler och framför allt tyngre matematiska modeller för att skatta utfallet av matcher. I detta examensarbete används Pi-ratingsystemet som går ut på att varje lag får en rating för hur bra man är på hemma- respektive bortaplan. Som en utveckling av den ursprungliga Pi-rating modellen används det i detta arbete tre olika modeller för att prediktera lagens framtida rating. Modellerna som används är enkelt glidande medelvärde, enkel exponentiell utjämning och en ARIMA-modell. En lösning på hur nya lag som inte spelade i ligan föregående år ska behandlas föreslås också. Avslutningsvis diskuteras olika investeringsmetoder som kan användas för att använda resultat från modellerna på marknaden för vadslagning. Resultatet visar att en spelstrategi som utnyttjat Kellys formel ger störst avkastning för kalibreringsdatat. När denna strategi används på matcher utanför kalibreringsåren visar resultatet på en mycket låg vinst och framför allt att vinsten under lång tid är negativ, vilket från en investeringssyn inte är något man önskar. Sammanfattningsvis är denna metod inte i sig själv tillräckligt bra för att ge en säker avkastning men är en bra grund som kan byggas ut för att ta hänsyn till fler faktorer och då ge möjlighet till stabilare och mer långsiktiga vinster. / To predict a soccer game in advance is something that has been done by most people. If the prediction is the result of an advanced mathematical formula or just ha pure guess done on your favorite team is very different. Since the computer power in recent years has greatly improved the number of mathematical approaches has increased and it is especially the computational heavy models that have increased in number. In this thesis the Pi-rating system is used it gives each team a home and away rating that describe how good/bad they are compared to the average competing team. As an extension of the original Pi-rating model, in this thesis time series analysis is used to predict future values of the teams rating, three different methods are tested and they are simple moving average, simple exponential smoothing and an ARIMA-model. A solution to how new teams that did not play in the league last year should be handled is also suggested. Finally a breath discussion and test of different investment methods that can be applied on the final model to be used on the sport betting market. The results show that the greatest returns on the calibration data is achieved when Kelly’s formula is used as an investment method on an ARIMA(0,1,1)-model, but when this strategy is used outside calibration data, the result shows a very low profit and the method  fails to give a stable long term return, which from an investment point of view is not desirable. The conclusion is that this method is not in itself good enough to provide a safe return but is a good foundation that can be expanded to take more factors into account, and then hopefully give bigger and more stable winnings.