# Econometric: Standard Deviation and Volatility Essay

Words: 3904
Pages: 16

ETF 5300 Applied Financial Econometrics, S2, 2013
Project One
Introduction
The dispersion of asset price returns can be measured by volatility. It is important to recognize the volatility of foreign exchange rate when doing risk management and policy evaluation. Volatility process provides information about how news affects asset prices and how markets process that information. Not only the expected return but also the trading strategy’s exposures to risk during high volatility periods need to be considered for traders and regulators.
In this report, we focused on the exchange rate of Australian dollars to US dollars from 02/01/2007 to 17/12/2010. The total 1,000 observations can be divided into two parts, in-sample period from 02/01/2007 to 22/11/2010 and out-of-sample period from 23/11/2010 to 17/12/2010.The data was downloaded from website: www.federalreserve.gov/ releases/h10/hist/. We omitted trading days that display either too many missing values or low trading activity as they will provide poor estimates of volatility. Also, week-ends and certain fixed and irregular holidays were deleted.
There are five parts in this report which are model selection for conditional mean, model selection for conditional volatility, main findings, conclusion and recommendations.

Model selection for the conditional mean:
From the plot of the log (E AUD/USD) (Graph 1), it can be found that this series seems to be non-stationary. This can be examined by the unit root test. The unit root test with intercept for the log (E AUD/USD)) has a probability of 0.6459(Graph 3), which is more than α=5%, then do not reject the null hypothesis of unit root. That means the log (E AUD/USD) is non-stationary. Then, test the correlogram of the first difference of log (E AUD/USD) (Graph 2). The graph seems like stationary and then do the unit root test to confirm that. As the p-value (graph 5) smaller than 5%, then conclude there is no unit root and it is stationary. Next, do the detrend and repeat the above steps to investigate whether it is trend stationary or differenced stationary. After detrended, the plot shows that it is not stationary (Graph 6). However, both the correlograms and unit root test proved that the detrended log (Graph 7-10) (exchange rate) has unit root and conclude it is stationary after detrend and the log (exchange rate) is differenced stationary.
Moving along with further investigation of the returns, the autocorrelation function of the price series is non-dampening as the number of lags increase. This is a characteristic of a non-stationary series. In fact, the ACF and PACF of the first lag are 0.993, which suggests that the series may follow a unit root process; PACF cuts off after the first lag while there is no white noise in the correlogram of log (E AUD/USD) (Graph 2)
Meanwhile, from Graph 11, the ACF of the return series suggest that there is no correlation in returns over time, this suggests that the returns process is a white-noise process. It also supports the weak-form efficient market hypothesis for the E AUD/USD .
Time series plot of the return series for E AUD/USD shows in Graph 12, the return series vary around a constant, near zero mean (mean stationary). In the middle of 2008, E AUD/USD has a relatively high volatility; on the contrary, in 2007 and 2010, the E AUD/USD has relatively low volatility. There is also evidence of volatility clustering as small returns are followed by small returns (small volatility) in 2007 &2010 and large returns follow large returns (high volatility period) in 2008.
To make a clearly characteristics and other stylized facts of the returns distribution, we then do a histogram and descriptive statistics, which are shown in Graph 13. Overall, the histogram plot of the return series is the bell-shaped, similar to the shape of normal distribution. Skewness statistic is 0.7175, which indicates the return distribution is positively skewed. The histogram confirms this