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Mathematics & Economics
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Research Paper
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Assessment of Stylistic Facts of Time Series Data from Stock Prices (Research Paper Sample)

Instructions:

Time series data has been collected on one variable for a period of time. The data on the variable could be
either undertaken daily, monthly, quarterly, or even annually. According to Cont (2001), the data is expected to
exhibit a certain set of properties. Studies using time series analysis have been seen to follow a certain pattern
of results which have helped assert the properties. According to Cont (2001), there has been 11 major
assumptions that have been related to time series analysis. This assumptions include; heavy tails, absence of
autocorrelation, gain/loss asymmetry, aggregation Gaussianity, intermittency, volatility clustering, conditional
heavy tails, slow decay of autocorrelation, leverage effect, volume/volatility correlation, and asymmetry in time
scale.
The current analysis would review 8 major assumptions including; heavy tails, absence of autocorrelation,
intermittency, volatility clustering, volume/volatility correlation, aggregation Gaussianity, and conditional
heavy tails.

source..
Content:


ASSESSMENT OF STYLISTIC FACTS OF TIME SERIES DATA FROM STOCK PRICES OF GOLDMAN SACHS GROUP
STUDENT NAME:
STUDENT ID:
DATE:
Executive summary
Time series data has been seen to exhibit a wide range of fact which have been referred as the major properties of the data. Cont. has in his work discussed 11 of the facts which have been seen to apply to most data sets. In financial data, time series data has been seen to exhibit unit roots thus following a volatility trend.
The current essay assessed eight of the 11 facts which were found to consider with the assumptions of Cont. and relevant to the Goldman Sachs Group (GS) market prices. The results revealed that the assumption fit for the financial information. Main findings showed that the data had no autocorrelation, if had increasing variance, the volume/ volatility correlation was negative, the data exhibited aggregation Gaussianity, and there were heavy tails which persisted even after correction for autocorrelation. The major implication of the analysis to the firm was the high expected uncertainty and risk as it is hard to determine with certainty the future market prices. In addition, the sample results are hard to generalise on the whole population to to evidence of possible kurtosis.
Introduction
Time series data has been collected on one variable for a period of time. The data on the variable could be either undertaken daily, monthly, quarterly, or even annually. According to Cont (2001), the data is expected to exhibit a certain set of properties. Studies using time series analysis have been seen to follow a certain pattern of results which have helped assert the properties. According to Cont (2001), there has been 11 major assumptions that have been related to time series analysis. This assumptions include; heavy tails, absence of autocorrelation, gain/loss asymmetry, aggregation Gaussianity, intermittency, volatility clustering, conditional heavy tails, slow decay of autocorrelation, leverage effect, volume/volatility correlation, and asymmetry in time scale.
The current analysis would review 8 major assumptions including; heavy tails, absence of autocorrelation, intermittency, volatility clustering, volume/volatility correlation, aggregation Gaussianity, and conditional heavy tails.
Literature Review
Time series data facts assume aggregation Gaussianity. In this assumption, argues that as time increase, the distribution of the data is likely to follow a normal distribution. Secondly, the time series data is expected to have no autocorrelation. Cont (2001), argued that in cases, of autocorrelation they have been seen to be insignificant. Third, there is an argument of heavy tails which argue that the distribution of the data is biased with flat tails. Fourth is the gain/loss asymmetry where the argument is based on drifts of the stock. Cont (2001) alleged that the downturn in prices are expected to be high as compared to the upward movement. In addition to the assumptions, there is the intermittency assumption which rates the priorities of high variability with persist of burst in the time scale data. Sixth, is the volatility clustering assumption which argue for positive autocorrelation for close time periods (Andersen et.al, 2001). In addition, to it he put forth the assumption of conditional heavy means which depict heavy tails even after volatility has been controlled. The eight assumption relies on slow decay of autocorrelation where the autocorrelation is expected to diminish as time increases. The ninth assumption lies on leverage effect where the volatility of assets is expected to be negatively correlated with assets return. In addition, volume/volatility correlation where there is expected negative correlation between the two. Finally, he alleged for asymmetry in time scale where there has been depicted fine-scale (Cont, 2001).
RESULTS AND DISCUSSIONS
Models
There are different models that are used in determination and forecast using time series data. Auto regression has been used mainly where the past values of the variable being determined are used. For instance the lag of a stock price occurring in a given time are used to determine the effective or the amount if stock price in a given time period (Osisanwo & Atanda, 2012). Therefore the past values of Y including yt-1, yt-2.... are used to forecast the value of Yt. Therefore making use of auto regression models, the values of Y at a given time period are regressed against their own lagged values. Different orders can be used in the modes given by order 1,2,3,4.....n. making use of the GS data, the analysis was run for different orders and results were presented in the tables below;
Using order 1 (where the lag is Y(t-1).
We are under a null hypothesis that time lag has no significant influence on the stock prices of GS Company (Goldman Sachs Group) at a given time. Making use of Autoregressive model order 1, the analysis is conducted in stata. The results reveal that the time lag has a significant influence as dictated by the significant p-value. Thus we reject the null and accept the alternative hypothesis. Thus conclude that the time lag has a significant influence on stock prices that would occur in a given time.
As shown in the table above, making use of lag order 1, the adjusted R-squared is 99.66. This means that the value of stock prices in a past period of order 1 are able to explain variability in daily stock growth rate by about 99.66%. The F-value is significant an indication that the model is able to adequately fit the data and thus can be used accordingly. The coefficient of Y lagged with one order of time is significant. This is to mean that as we increase the lag period by one time unit, the stock prices of the company are expected to grow by about 99.7%.
Using order 2 (where the lag is Y(t-2).
Combining the effect of two time lags, we use the null hypothesis of existence of no significant influence of past stock prices with a price difference order 1 and 2. Therefore we state a null of the coefficient of lag one to zero and that of lag two to zero. Making us of autoregressive model order 1 and 2 we examine the results using GS in stata. The results are however significant at lag one and not significant at lag two as shown in the table above. This is an indication that we reject the null of coefficient of lag one being zero, but fail to reject the hypothesis that coefficient of lag two equals zero. Thus we conclude that stock prices in a given time period are significance influenced by first order time prices and not the second order.
Looking at the mode, addition of one more variable to the model the adjusted R-squared improves to 0.9969. This is an indication that the both variables combines, they are able to explain about 99.69% of the variability in stock prices of GS Company. The probability of F-value is significant an indication that the model parsimony is fit and thus the model is able to appropriately fit the data. Lay of order 1 is significant. This is an indication that a reduction of the value of y by one order, the stock prices could increase by about 99.5%. We are also 99% certain that the prices would increase by about 946% to 100% of the stock value observed in the last period.
Using order 3 (where the lag is Y(t-3).
With a null of not effect of lag one, two, and three on the stock prices, the Autoregressive model order three used. The results reveals that the coefficient of order one are significant with those of order to and three being insignificant. We therefore reject the null that the coefficient of order one equal zero, but fail to reject the null of order two and three being zero. We thus conclude that lagging time period once has a significant influence on the stock prices to occur at a given time.
The model F-value is significant an indication that the model is able to fit the data and thus could be seen to explain variability in stock prices (Osisanwo & Atanda, 2012). Using the three combined effect, the adjusted R-squared improves to 99.70. This is an indication that the three variables combined, they are able to explain about 99.7% of the variability in future stock prices. Lag order one is significant. This is an indication that using stock prices in the past one period would help forecast future prices. That is a lag with one unit, would increase the future stock prices by 102.2%.
Using order 4 (where the lag is Y(t-4).
Using the null that lagging time from order one to four has no significant influence on future stock prices. The fourth order autoregressive model is use. The results show that lag order one is significant and thus we reject the null. However, for order two, three and four, the null hypothesis is accepted. We thus conclude that using the past stock prices of the last period would help increase stock prices of the future by 104%.
The model fitness is ok with a significant f-value. The variability as explained by adjusted R-squared is 99.69. A decline from the AR3, but similar variability as explained by AR2.
Testing the stylistic facts
Cont (2001) stated about 11 facts about time series data. These fact have been widely accepted in many scenarios and thus the current analysis will make use stock prices from GS Company to assert the work of Cont.
1. Absence of autocorrelation
According to the work of Cont backed with other assessment on financial data that have been assessed in the past, the time series data has been seen to exhibit no autocorrelation and where they exist, they are insignificant. Especially for longer period exceeding 20 days, the linear autocorrelation is not persis...

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