This thesis aims to fit and compare different time series models namely the ARIMA-model, conditional heteroscedastic models and lastly a dynamic regression model with ARIMA error to Bitcoin closing price data that spans over 5 consecutive years. The purpose is to evaluate if the sanction on Russia had any effect on the cryptocurrency Bitcoin. After giving a very brief introduction to time series models and the nature of the error term, we describe the models that we want to compare. Quite early in on, autocorrelation was detected and that the time series were nonstationary. Additionally, as we are dealing with financial data, we found that the best alternative was to transform the data into logarithmic return and we then took the first difference. As we then detected a very large outlier, we decided to replace the extreme value with the mean of the two adjacent observations as we suspected it would affect the forecast interval. The dataset with first differenced log-returns was used in the ARIMA model but it turned out that there was no autocorrelation which indicated that returns in financial assets are uncorrelated across time and therefore unpredictable. The conditional heteroscedastic models, the ARCH and the GARCH models turned out to be best suitable for our data, as there was an ARCH-effect present. We could conclude that the GARCH(1,1) model using student t-distribution had the best fit, which had the lowest AIC and the highest log likelihood. In order to study the effect of the sanctions on Bitcoin volatility a dynamic regression model was used by allowing the error term to contain autocorrelation and include an independent dummy variable. The model showed that the Russian invasion of Ukraine did not, surprisingly, have any effect on the Bitcoin closing price.

Today, there is an overwhelming amount of data that is being collected when it comes to financial markets. For forecasting stock indexes, many models rely only on historical values of the index itself. One such model is the ARIMA model. Over the last decades, machine learning models have challenged the classical time series models, such as ARIMA. The purpose of this thesis is to study the ability to make predictions based solely on the historical values of an index, by using a certain subset of machine learning models: a neural network in the form of a Gated Recurrent Unit (GRU). The GRU model’s ability to predict a financial market is compared to the ability of a simple ARIMA model. The financial market that was chosen to make the comparison was the American stock index Nasdaq-100, i.e., an index of the 100 largest non-financial companies on NASDAQ. Our results indicate that GRU is unable to outperform ARIMA in predicting the Nasdaq-100 index. For the evaluation, multiple GRU models with various combinations of different hyperparameters were created. The accuracies of these models were then compared to the accuracy of an ARIMA model by applying a conventional forecast accuracy test, which showed that there were significant differences in the accuracy of the models, in favor of ARIMA.

The majority of manufacturers provide their customers with volume discounts for placing repeat purchases or placing larger orders. In today's highly competitive market, the topic of how precisely a big number of products should be grouped together naturally emerges.\\In this context, three research questions that were directly relevant to the setting were formulated and their answers were provided. In order to achieve this goal, a number of experiments were carried out. In this particular instance, an algorithm was developed that determines the order combination that is mathematically superior to all others. In this context, an annual order cost saving of 1.33\% could be achieved based on the orders from the year 2021. This could be accomplished without the utilisation of heuristics for a limited number of products at most. In addition, a number of other heuristics have been devised for higher order combination sets. In addition, two other approaches to demand forecasting were investigated, and it was discovered that the time series in this particular instance was insufficient for the application of an RNN-LSTM model.

The goal of this thesis is to be able to predict customer traffic at postal service points. The expectation is that when customers are made aware of queue times at the service points, they will redistribute themselves to avoid standing in line. This boils down to a form of time series prediction problem. When working with time series prediction, there are potentially other factors that may help the models make a more accurate prediction. Factors that may affect people’s behavior are unlimited, but this thesis examines the effect of the external calendar variables (weekday, date and public holiday) and weather variables (temperature, precipitation and sun, among others) when making the predictions. Non-linear models are examined, with the focus on Multilayer Perceptrons (MLPs) and Long Short-Term Memory (LSTM) models that have shown promising results in time series prediction, and these models are referred to as Artificial Neural Networks (ANNs). Support Vector Regression (SVR), Autoregressive Moving Average (ARIMA) and statistical average models are used for comparison. The results show that using external variables as additional input to LSTM, MLP and SVR models increases the test prediction performance. Further, the MLP model generally performs better than the LSTM models. The results are acquired using six postal service points, and the final results are based on a six-fold cross validation across all six service points. The LSTM and MLP are able to better use the external variables and show greater adaptability during e.g. public holidays, compared with the SVR model. The ARIMA and historical average model show less accurate predictions compared with the aforementioned models. / Målet med detta examensarbete är att förutspå kundtrafik hos postserviceställen. Förhoppningen är att kunderna omfördelar sig själva om de får tillgång till kundtrafikprognoser för att undvika stå i kö. Detta resulterar i ett tidsserie-förutsägelseproblem. Vid sådana problem finns det potentiellt andra faktorer som kan påverka modellernas prediktioner positivt. Antalet faktorer som påverkar människors beteende är obegränsat, men detta examensarbete undersöker effekterna av att använda externa kalendervariabler (veckodag, datum och röd dag) och vädervariabler (temperatur, nederbörd och sol, bland annat). För att göra prediktionerna används främst de icke-linjära modellerna Multilayer Perceptron (MLP) och Long Short-Term Memory (LSTM), som båda refereras till som Artificial Neural Network (ANN). Båda modellerna har visat lovande resultat i liknande problem. Utöver dem används även modellerna Support Vector Regression (SVR) och Autoregressive Moving Average (ARIMA) samt det historiska genomsnittet som jämförelse. Resultaten visar på att om LSTM-, MLPoch SVR-modellerna får externa variabler som tilläggsinput så förbättras modellernas förutsägelser. Vidare presterar MLP-modellen generellt bättre än LSTMmodellen. Resultaten är skapade genom att använda sex stycken postserviceställen och de slutgiltiga resultaten är baserade på en 6-vägs korsvalidering för samtliga serviceställen. LSTMoch MLP-modellerna är bättre på att använda informationen från de externa variablerna och visar på större anpassningsförmåga, under till exempel röda dagar, jämfört med SVR-modellen. ARIMA-modellen och den historiska genomsnittsmodellen skapar sämre prediktioner än de förutnämndamodellerna.

I och med digitaliseringen förändras samhället snabbare än någonsin och det är viktigt för företag att hålla sig uppdaterade för att kunna anpassa sin verksamhet till en marknad som hela tiden utvecklas. Det existerar en uppsjö av business intelligence modeller för just detta ändamål, och prediktiv analys är en central del bland dessa. Fokus i denna rapport ligger i att undersöka i vilken utsträckning tre olika prediktiva analysmetoder lämpar sig för ett specifikt uppdrag gällande månadsprognoser baserat på klickdata från Flygresor.se. Målet med rapporten är att kunna redogöra för vilken av metoderna som fastställer den mest precisa prognoser för given data och vilka karakteristiska drag i datan som bidrar till detta resultat. Vi kommer att tillämpa de prediktiva analysmodellerna Holt-Winters och ARIMA, samt en utbyggd linjär approximation, på historisk klickdata och återge arbetsprocessen samt utifrån resultatet beskriva vilka konsekvenser datan från Flygresor.se förde med sig. / With digitization, society changes faster than ever and it’s important for companies to stay up to date in order to adapt their business to a constantly changing market. There exists a lot of models in business intelligence, and predictive analytics is an important one. This study investigates to what extent three different methods of predictive analytics are suitable for a specific assignment regarding monthly forecasts based on click data from Flygresor.se. The purpose of the report is to be able to present which of the methods who determines the most precise forecasts for the given data and what trends in the data that contributes to this result. We will use the predictive analytics models Holt-Winters and ARIMA, as well as an expanded linear approximation, on historical click data and render the work process as well as what consequences the data from Flygresor.se brought with them.

This thesis compares the results of the performance of the statistical Autoregressive integrated moving average (ARIMA) model and the neural network Long short-term model (LSTM) on a data set, which represents a market index. Both models are used to predict monthly, daily, and minute close prices of the OMX Stockholm 30 Index. Chosen data were preprocessed, models were fitted to data and their prediction was evaluated and compared. To evaluate forecast accuracy as well as to compare two models fitted to a financial time series, we have used the two performance measures: mean square error (MSE) and mean absolute percentage error (MAPE). In addition, the computation time of fitting models was measured in this thesis to evaluate and compare the computational workload associated with the two models. Also, other factors were discussed, such as the number of parameters and explainability. The analysis revealed that the minute and the daily data of the OMX 30 Stockholm index closely resembled white noise, indicating random fluctuations. However, for the monthly data, the LSTM model outperformed the ARIMA model in terms of MSE, with values of 15,230 and 14,380, respectively. Additionally, the LSTM model demonstrated superior capability in capturing the dynamics of price movement compared to ARIMA. Regarding MAPE, both models exhibited similar values, with ARIMA at 4.8 and LSTM at 4.9. In addition, the ARIMA model had significantly fewer parameters compared to the LSTM model and offered the advantages of being more transparent and easier to interpret.

Accurately predicting the S\&P 500 index means knowing where the US economy is heading. If there was a model that could predict the S\&P 500 with even some accuracy, this would be extremely valuable. Machine learning techniques such as neural network and Random forest have become more popular in forecasting. This thesis compares the more traditional forecasting methods, ARIMA, Exponential smoothing, and Naïve, versus the Random forest regression model in predicting the S\&P 500 index. The models are compared using the scale measures MAE and RMSE. The Diebold-Mariano test is used to evaluate if the model's forecasts significantly have better accuracy than the last known observation (Naïve method). The result showed that the Random forest model did outperform the other models regarding the RMSE and MAE values, especially on a two-day forecast. Furthermore, the Random forest model was significantly better on all horizons on a five percent significance level, meaning that the model had a better forecast accuracy than the last known observation. However, further research on this subject is needed to ensure the effectiveness of the Random forest model when forecasting stock market indices.

The purpose of this thesis was to investigate whether some successful ideas in NLP, such as word2vec, are applicable to time series prob- lems or not. More specifically, we are interested to assess a combina- tion of previously proven methods such as SAX and Word2vec. Based on a rolling window approach, we applied SAX to create words for each window. These words formed a corpus on which we performed Word2vec, which served as inputs in a time series forecasting setting. We found that for forecasting horizons of longer length, our proposed method showed an improvement over statistical models under certain conditions. The findings suggest that bringing tools from the natural language processing domain into the time series domain may be an ef- fective idea. Further research is necessary to broaden the knowledge of these types of methods by testing alternative options for the cre- ation of words. Hopefully, this work will motivate other researchers to investigate this type of solution further.

Global food prices are currently rising at a rapid pace. The current supply chain involves a number of different steps, where each step involves a price surcharge that is ultimately paid by the consumer. Modern technology, such as machine learning and smart logistics, enables alternative supply chains. This report examines the possibility of designing a model that, with the help of scenarios of change based on previous studies and the taskmaster’s vision, can make predictions for future food prices. The report was based on the supply chain and current prices for potatoes. The models used are ARIMA, SVR with different cores, linear regression, Ridge regression and Lasso regression. The models are evaluated with the error measurements Mean Absolute Error, Mean Squared Error, Root Mean Squared Error and R2. The best-performing models, with which the prediction was then performed, were ARIMA and SVR with a linear core. The predictions and calculations showed drastically reduced food prices and a large reduction in unnecessary food waste, especially in the scenario that involves an overall change of the supply chain. This has major macroeconomic effects, as food prices affect inflation. The analysis also shows the importance of the industry’s players working with analysis and strategy to handle a future shift that entails higher uncertainty in the market. There are uncertainties about the effect on other supply chains, as well as the net effect of a shift as the costs for this are unknown. / I dagsläget stiger livsmedelspriserna globalt i hög takt. Den nuvarande försörjningskedjan innebär många olika steg, där varje steg innebär prispåslag som till slut betalas av konsumenten. Modern teknik, som maskininlärning och smart logistik ger upphov till alternativa försörjningskedjor. Denna rapport undersöker möjligheten att utforma en modell som, med hjälp av omställningsscenarion baserade på tidigare studier och uppdragsgivarens vision, kan göra prediktioner för framtida livsmedelspriser. Rapporten baserades på försörjningskedjan och aktuella priser för matpotatis. De använda modellerna är ARIMA, SVR med olika kärnor, linjär regression, Ridge regression samt Lasso regression. Modellerna utvärderas med felmåtten Mean Absolute Error, Mean Squared Error, Root Mean Squared Error samt R2. De bäst presterande modellerna, som prediktionen sedan utfördes med, var ARIMA och SVR med linjär kärna. Prediktionerna och uträkningarna visade på drastiskt sänkta matpriser och en stor sänkning av onödigt matsvinn, framför allt vid det scenario som innebär en övergripande omställning av försörjningskedjan. Detta för med sig stora makroekonomiska effekter, då livsmedelspriset påverkar inflationen. Analysen visar även på vikten av att branschens aktörer arbetar med analys och strategi för att hantera ett kommande skifte som innebär en högre osäkerhet på marknaden. Osäkerheter finns kring effekten på andra försörjningskedjor, samt nettoeffekten av en omställning då kostnaderna för denna är okända.

The United States Defense Industrial Base (USDIB) is an essential industry to both the economic prosperity of the US and its strategic control over many advanced military systems and technologies. The USDIB, which encompasses the industries of aerospace and defense, is a volatile industry - prone to many internal and external factors that cause demand to ebb and flow widely year over year. Among the factors that influence the volume of systems the USDIB delivers to its international customers are the arms export controls of the US. These controls impose a divergence from the historical US foreign policy of furthering an open exchange of ideas and liberalized trade. These controls, imposed by the Departments of Commerce, Defense, and State rigidly control all international presence of the Industry. The overlapping controls create an inability to conform to rapidly changing realpolitiks, leaving these controls in an archaic state. This, in turn, imposes a great deal of anxiety and expense upon managers within and outside of the USDIB. Using autoregressive integrated moving average time-series analyses, this paper confirms that the implementation of or amendment to broad arms export controls correlates to significant and near immediate declines in USDIB export volumes. In the context of the US's share of world arms exports, these controls impose up to a 20% decline in export volume.