# Time Series Modelling

Coursework Brief:
You must be aware that only you share responsibility for any academic integrity breaches or other issues that may arise from your coursework submission. Rubric I do expect tables / graphs / diagrams in this assignment (embedded in the main text).

Each table, graph or diagram will count as 25 words. Any table/graph must be explained contextualizing the results to the context of the question. Remember that the graphs and tables you present are properly contextualized and form an important aspect of our explanations. Additional graphs and tables can be put in the appendix as well as the output from any statistical software you have used for the analysis.

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There are TWO compulsory questions for this Assignment.
Question One
Background information for Question One
In Question One, we have provided cross-market time series data for Bitcoin (one of the popular cryptocurrencies floating in the market). The Bitcoin is traded in various currencies, such as in Euros, USD, Korea, etc. The data have been collected from Coincheck (one of the platforms that provides aggregate price data for Bitcoin). In the Blackboard site of the course (see Assignment folder), we have included Bitcoin price data for six exchange markets (Europe, USA, Australia, Korea, Japan, Indonesia).

You can choose ANY file(s) depending on your interest. Eviews, Stata, R, Python or other any econometric software may be used for empirical estimation purpose.

Tasks for Question One
(1)By plotting the selected Bitcoin price series explain if you find any ‘trend’ in the price behavior. Use Hodrick-Prescott (H-P) Filtering Technique and Hamilton Filtering Techniques respectively to extract the ‘cycles’ from the ‘trends’. Plot the Autocorrelation Function and comment on the persistence behavior of the series.

(2)Test for (non-)stationarity in the selected series by using Augmented Dickey-Fuller, Phillips-Perron, and KPSS tests. Use options of intercept with and without trend term to compare your results. What implications do the ‘presence or absence of a unit root’ imply for the selected Bitcoin price regarding ‘weak, strong, semi-strong efficiency’  of the Bitcoin market?

(3)Assume that the Bitcoin series you selected is neither I(1) nor I(0). Then what would an I(d)with 0<d<1 assumption imply for the Bitcoin market with respect to Efficient Market Hypothesis?

(4)Use any THREE Bitcoin prices from the list and find if there is any error-correction mechanism at work among them. Describe in detail, with regard to these specific selected series, a 3-variables cointegration and Vector Error Correction system.

[50 marks]

Question Two
Background information for Question Two
Topics
Your task is to test a hypothesis (see topics below). You need to discuss the following steps:
(1)data collection (e.g. method of sampling, data sources, selection criteria);
(2)definition of variables (e.g. control variables);
(3)model specification (e.g. Unit root, Cointegration framework; ARCH/GARCH models);
(4)interpretation of findings and conclusion.

To illustrate your empirical findings, you are expected to use tables and figures.
Recommended data sources: Datastream, Bankscope, FAME, Yahoo Finance

Please select one of the following topics / hypothesis.

2.1. Economic policy uncertainty is known to exert a statistically significant and negative impact on bond yields. This is consistent with the theory that investors tend to increase their demands in bonds during periods of higher economic or government policy uncertainty and thereby increasing bond prices and reducing their yields.

HINT: You can examine the relationship between Economic Policy Uncertainty (EPU) of a country (see data here: https://www.policyuncertainty.com/) on future bond excess return across maturities and holding periods for the chosen markets.

You can collect bond data from the database of the US Treasury for the US data and the Bank of England for the UK data, for instance. The data of US government bonds are updated daily at website: https://www.treasury.gov/resource-center/data-chart-center/interest-rates. The data of UK government bonds are daily updated at website: https://www.bankofengland.co.uk/statistics/yield-curves. Visit https://en.wikipedia.org/wiki/Time_series for more details.

You can try to use unit root tests (to identify non-stationarity) and cointegration methods to understand the nature of co-movement between the variables.

2.2. Test the following hypothesis: “(Regional) housing prices depict strong spillover effects”.

HINT: You can calculate volatility in housing prices (within a country across regions or if you want across countries within a common economic union, such as Europe Economic Union). Try to use different types of GARCH models to estimate spillover effects (read literature).
[50 marks]

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