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# 统计代写|时间序列和预测代写Time Series & Prediction代考|QMS517 Performance Analysis

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## 统计代写|时间序列和预测代写Time Series & Prediction代考|Performance Analysis

This section attempts to compare the relative performance of the proposed five techniques with 27 other techniques [21, 27, 31, 32, 36, 47] using RMSE as the metric for comparison. Table $2.5$ provides the results of comparison for the period 1999-2004 with mean and standard deviation of all the RMSEs obtained for the above period. It is apparent from Table $2.5$ that the entries in the last row are smaller than the entries above. This indicates that that RMSE for each column on the last row of Table $2.5$ being the smallest, the proposed method 5 seems to outperform the other techniques (calculated with respect of mean of 6 years RMSE) by at least $23 \%$, encountered in method-19 in Table $2.5$.

We here use paired t-test [64] to examine the statistical confidence on the results of prediction by different algorithms using RMSE as the metric. Let, $H_o$ be the null hypothesis to compare two algorithms’ performance, where one is the reference algorithm, while the other is any one of the existing algorithms. Here, we consider the proposed algorithm as the reference algorithm. Thus, $H_o=$ Performance of algorithm $A$ and reference algorithm $R$ are comparable.

Let $A$ be the algorithm by Chen et al. [47]. To statistically validate the Hypothesis $\mathrm{H}_{\mathrm{o}}$, we evaluate t-measure, given by
$$t=\frac{\left(m_A-m_R\right)}{\sqrt{s_A^2+s_R^2}},$$
where $m_A$ and $m_R$ are the mean values of the distributions of RMSE obtained by algorithms A and R respectively with equal sample size in the two distributions, and $s_A$ and $s_R$ are the standard deviations of the respective samples obtained by algorithms $A$ and $R$.

## 统计代写|时间序列和预测代写Time Series & Prediction代考|Conclusion

This chapter introduced a novel approach to stock index time-series prediction using IT2Fs. Such representation helps overcoming the possible hindrances in stock index prediction as introduced in the introduction. Both triangular and Gaussian MFs along with provision of their adaptation have been introduced to examine their relative performance in prediction. The strategy used to consider secondary to main factor variation has considerably improved the relative performance of the stock
index time-series prediction. A thorough analysis of results using RMSE as the metric indicates that the proposed methods outperform the existing techniques on stock index prediction by a considerable margin $(\geq 23 \%)$. Out of the five proposed methods, the method employing triangular MF with provision for its adaptation yields the best performance following the prediction of TAIEX stock data for the period of 1999-2004 with DOWJONES and NASDAQ together as the composite secondary index. A statistical analysis undertaken with paired t-test confirms that each of the proposed algorithms outperforms most of the existing algorithms with root mean square error as the key metric at $95 \%$ confidence level. With an additional storage of fuzzy logical implication rules and frequency of occurrences from CSVS to MFVS for $d=1,2, \ldots, k$, we would be able to predict the close price on the next day, next to next day and the like from today’s close price. Further extension of the proposed technique can be accomplished by using General Type-2 fuzzy sets, which is expected to improve performance at the expense of additional complexity.

## 统计代写|时间序列和预测代写Time Series \& Prediction代考|Performance Analysis

$$t=\frac{\left(m_A-m_R\right)}{\sqrt{s_A^2+s_R^2}},$$

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