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August 8th, 2017 
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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 “Average monthly temperatures in Edgbaston” for the year range “2008–2014” 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 “Exchange rates monthly data – Pounds vs. Euro” for the year range “2008-2014” 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)
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