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# 数据科学代写|金融统计代写Financial Statistics代考|CMSE11086 Inference on the Gold Price Data (In US Dollars)

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## 数据科学代写|金融统计代写Financial Statistics代考|Inference on the Gold Price Data (In US Dollars) (1980–2013)

Gold price data, say $x_{t}$, were collected per ounce in US dollars over the years $1980-2013 .$ These were transformed as $z_{t}=100\left(\ln \left(x_{f}\right)-\ln \left(x_{t-1}\right)\right)$, which were then “wrapped” to obtain $\theta_{t}=z_{t} \bmod 2 \pi$ and finally transformed to $\hat{\theta}=\left(\theta_{t}-\bar{\theta}\right) \bmod 2 \pi$, where $\bar{\theta}$ denotes the mean direction of $\theta_{t}$ and $\hat{\theta}$ denotes the variable thetamod as used in the graphs. The Durbin-Watson test performed on the log ratio transformed data shows that the autocorrelation is zero. The test statistic of Watson’s goodness of fit Jammalamadaka and SenGupta (2001) for wrapped stable distribution was obtained as $0.01632691$ and the corresponding p-value was obtained as $0.9970284$, which is greater than $0.05$, indicating that the wrapped stable distribution fits the transformed gold price data (in US dollars). The modified truncated estimate $\hat{\alpha_{1}^{*}}$ is $0.3752206$ while the estimate by characteristic function method is $0.401409$. The value of the objective function using the characteristic function estimate is $2.218941$ while that using our modified truncated estimate is 2.411018.

## 数据科学代写|金融统计代写Financial Statistics代考|Inference on the Silver Price Data (In US Dollars) (1980–2013)

Data on the price of silver in US dollars collected per ounce over the same time period also underwent the same transformation. The Durbin-Watson test performed on the log ratio transformed data shows that the autocorrelation is zero. Here, the Watson’s goodness of fit test for wrapped stable distribution was also performed and the value of the statistic was obtained as $0.02530653$ and the corresponding $p$-value is $0.9639666$, which is greater than $0.05$, indicating that the wrapped stable distribution also fits the transformed silver price data (in US dollars). The modified truncated estimate of the index parameter $\alpha$ is $0.4112475$ while the estimate by characteristic function method is $0.644846$. The value of the objective function using the characteristic function estimate is $2.234203$ while that using our modified truncated estimate is $2.234432$.

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