Financial and Statistical Modelling The report: Find sources of real-life time series data and select two series of interest, one without seasonal effect and the other with seasonality. 1. For seasonal effect I have chosen the data of œAverage monthly temperatures in Edgbaston for the year range œ2008“2014 because this as shown in the graph portrays seasonality. Seasonality is visible in the graph as you can see that the trend is recurrent at given months. 2. For the non seasonal effect I have chosen the data of œExchange rates monthly data “ Pounds vs. Euro for the year range œ2008-2014 as it shows the non seasonal effect as seen in the graph provided. Trace the two series back in order to collect sufficient observations to perform a meaningful analysis. (This will require a minimum of 48 observations for data collected quarterly and a minimum of 72 for monthly data). Exchange Rates in Euro and Pounds 3. Investigate the background for each of the two series: what it represents, how the data are collected, if there have been changes in the way in which it was collected, what factors may affect the series, etc. In the scenario above, the projected data on Edgbaston monthly moving average Temperature (oC) demonstrates seasonality. If you think that other factors affect the series make sure that you collect data for those factors so you can include them later in the analysis as explanatory variables. Climatic changes tend to affect futuristic trends when it comes to monthly moving temperatures. The exchange rate on the other hand is affected by the market forces, demand and supply. The exchange rate has distinct and significant effect on growth. 5. For each of the series analyse the data and forecast the next three time points using a variety of forecasting techniques 6. Comment critically on your findings Scores of time series statistics follow recurring seasonal trends. For instance, yearly exchange rate will are highest during the winter that is December and Jan. In 2008, the Exchange Rate Euro vs. Pound was at 1.33879 while the temperature was at 4 degrees centigrade. During the summer holiday of 2008, the Exchange Rate Euro vs. Pound was at 1.26166 and 1.26096 during the month of July and August respectively, while the temperatures were all time high at 17 degree centigrade’s. Smoothing models demonstrates a linear upwards pattern of exchange rate over the time and a recurring trend or season in a given year. (For instance, exchange rate is highest during summer and the low season is represented. The report adopts a seasonal decomposition to separate those elements, hence cluster the series into the pattern effect and seasonal effects. The regression model presents one of the finest forecasts of the dependent variable (Y), based on the independent variable (X). Nevertheless, issues to with weather can be uncertain to forecast, hence demonstrating a significant variation of the visible points around the fitted regression line. i) Moving average and decomposition The moving average of exchange rate in Euros v. Pounds demonstrates a non-seasonality trend owing to a trend that is not repetitive. Edgbaston monthly averages temperature demonstrates a seasonal behavior owing to a repetitive trend. The trend has been visible during certain months. March of 2008 and 2009 exhibited a similar temperature. The same pattern is visible between august 2008 and 2009, December 2008 and 2009, Jan 2009 and 2010, March 2009 and 2010 and so forth. This trend is largely impacted by climatic variations, which is normally tied to annual cycles. The seasonality in this case is a regular fluctuation that is repeated year after year with a similar timing and intensity. ii) Regression analysis (including GAMLSS) Descriptive Statistics Mean Std. Deviation N Month 6.50 3.476 72 Edgbaston Monthly Average Temperatures 0C 9.81 4.895 72 Correlations Month Edgbaston Monthly Average Temperatures 0C Pearson Correlation Month 1.000 .214 Edgbaston Monthly Average Temperatures 0C .214 1.000 Sig. (1-tailed) Month . .035 Edgbaston Monthly Average Temperatures 0C .035 . N Month 72 72 Edgbaston Monthly Average Temperatures 0C 72 72 Model Summaryb Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Durbin-Watson R Square Change F Change df1 df2 Sig. F Change 1 .214a .046 .032 3.420 .046 3.372 1 70 .071 .814 a. Predictors: (Constant), Edgbaston Monthly Average Temperatures 0C b. Dependent Variable: Month Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. Collinearity Statistics B Std. Error Beta Tolerance VIF 1 (Constant) 5.007 .907 5.518 .000 Edgbaston Monthly Average Temperatures 0C .152 .083 .214 1.836 .071 1.000 1.000 a. Dependent Variable: Month Descriptive Statistics Mean Std. Deviation N Month 6.50 3.476 72 Exchange Rate 1.1850941 .05707804 72 Correlations Month Exchange Rate Pearson Correlation Month 1.000 -.022 Exchange Rate -.022 1.000 Sig. (1-tailed) Month . .426 Exchange Rate .426 . N Month 72 72 Exchange Rate 72 72 Model Summaryb Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Durbin-Watson R Square Change F Change df1 df2 Sig. F Change 1 .022a .001 -.014 3.500 .001 .035 1 70 .852 .782 a. Predictors: (Constant), Exchange Rate b. Dependent Variable: Month Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. Collinearity Statistics B Std. Error Beta Tolerance VIF 1 (Constant) 8.120 8.634 .940 .350 Exchange Rate -1.367 7.278 -.022 -.188 .852 1.000 1.000 a. Dependent Variable: Month The regression analysis ensures that unconditional volatility and the velocity of mean restrictions are constant. Additionally, large data are required to accurately classify different elements. Nevertheless, the slow moving pattern is mean reversion to a constant value and the notion that volatility procedure ultimately changes to a fixed level. iii) ARIMA models Fig 1: Showing Forecasted Birmingham Monthly Average Temperatures in the next 3 years Figure 2: Showing Forecasted Exchange Rate in the next 3 years To effectively fit the time series of exchange rate ARIMA model is applied. In every case, low frequency volatility is obtained, therefore it can be explained as the average of the daily return over a given time frame-annually. Changes in financial markets and levels are the main themes in this scenario. These aspects largely impact on the uncertainty of exchange rate, cash flow; risk premiums and effect stock volatility rely on the economic conditions. In line with this model, past studies have indicated a connection between business cycle and volatility; for instance, they show that financial recession as the main aspect affecting exchange rate uncertainties. On the contrary, under certain conditions, realized exchange rates can be considered as estimated awareness of unpredictability. Precariousness as well as exchange rates is potential aspects influencing financial market. Subsequently, empirical data shows a close relationship between exchange rates and macro economic instability. The exchange rate is estimated in pounds. Both predictors of economic measures or future condition of financial market are vital explanatory measures for low exchange rate. For instance, variables related to the financial policy and projected economic developments are important in assessing projected uncertainties regarding exchange rates. iv) Smoothing (including structural time series models) This time series represents a pattern of observations that are ordered in time. Intrinsic in the collection of stastical data over time is a form of indiscriminate deviation. Smoothing is largely employed to demonstrate an essential pattern of seasonality. Here the Smootthing method minimise irregularities in the time series statistics. TO ORDER FOR THIS QUESTION OR A SIMILAR ONE, CLICK THE ORDER NOW BUTTON AND ON THE ORDER FORM, FILL ALL THE REQUIRED DETAILS THEN TRACE THE DISCOUNT CODE, TYPE IT ON THE DISCOUNT BOX AND CLICK ON ˜USE CODE’ TO EFFECT YOUR DISCOUNT. THANK YOU