Time series Project Final

8/10/2019 Time series Project Final

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Abstract

This study objective to examine the relationship between gold prices, oil prices and BSE. Thisstudy important for the investor whose want to invest in real assets and financial assets. Thisstudy helps investor to achieve the portfolio diversification. This study uses the monthly data ofgold prices, BSE , and oil prices for the period of 2001 to 2014 (monthly). This study appliedDescriptive statistics, Augmented Dickey Fuller test, Johansen and Co-integration test, andcausality test to find relationship. This study concludes that Gold prices growth, Oil pricesgrowth and BSE return have no significant relationship in the long run . This study providesinformation to the investors who want to get the benefit of diversification by investing in Gold,Oil and stock market. In the current era Gold prices and oil prices are fluctuating day by day andinvestors think that stock returns may or may not affected by these fluctuations. This study isunique because it focuses on current issues and takes the current data in this research to help theinvestment institutions or portfolio managers.

IntroductionGold has been used in market since 1971 as commodity. The importance of gold has beenincreased in the present world due to the financial crisis in the present economic world. Gold has

been used around the world as an instrument for investment to hedge against inflation or in theform of jewellery. All these factors are the reason for hyping the demand for gold day by day. As

per world gold council gold demand in India is about to rise 33% by 2020.The cumulative annualdemand will be excess of 1,200 tonnes by 2020.Recently India has become the largest consumerof gold and price of gold is likely to breach Rs 32,000 mark in the next calendar year.

The investors are investing in the Gold. In the recent decade the gold prices and oil prices riseday by day. India is in possession of 557 tons of gold reserves. India is the 11th largest countryin the world having gold reserve. In Present situation gold has attracted the investors due to alittle chance to go better outcomes in the stock market investments due to fragile economic andfinancial position in India. In market where shares are traded, is called stock market or equity


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market. Investors are showing low interest in the stock markets and investing in highly solidinvestment like gold due to rising trend in gold prices.

In this new era of economic growth, the exceptional increase in the crude oil prices is one ofthe significant developments that affecting the global economy. Crude oil is an important rawmaterial used for manufacturing many goods, so that an extraordinary increase in the priceof oil is bound to warn the economy with inflationary tendencies. This paper has analyzed the

performance or the reaction of the stock market towards the crude oil price change. The purposeof this study is to explore the relationship between the Gold prices, Stock market return and Oil

prices. The data is taken from BSE return, Gold price and Oil prices from 2001 to 2014(monthly).This study applied Descriptive statistics, Augmented Dickey Fuller test Phillip Perron test,Johansen and Jelseluis Co-integration test to find relationship between oil prices and Gold

prices with BSE Returns.

Literature Review

The review of the different past studies can provide idea for understanding the situations andfinding on the different grounds by which the researcher elaborates the finding with logicalreasoning.

S. Kaliyamoorthy and S. Parithi (2012) have made a study to examine the relationship between gold price and stock market for the period from June 2009 to June 2010. They provethat there is no relationship with the stock market and gold price and stock market is not aground for rising gold price.

Gagan Deep Sharma and Mandeep Mahendra (2010) made a study to evaluate thelong-term relationship between BSE and Macro-economic variables (exchange rates, foreignexchange reserve, inflation rate and gold price) for the period from January 2008 to January2009 using multiple regression model. The study reveals that exchange rate and gold priceinfluences the stock prices in India.

Jesus Alvarez and Ricardo Solis (2010) presented empirical research on marketinefficiencies focuses on the detection of autocorrelations in price time series. In the case ofcrude oil markets, statistical support is claimed for weak efficiency over a wide range oftime-scales.

Radhika Pandey (2005) examined One of the significant developments affecting theglobal economy in the current scenario is the phenomenal increase in the crude oil prices andexplore the possible conflicts which policy makers experience while framing policies forcurbing the adverse impact of oil price hike.

A considerable number of studies on the relationship between crude oil price, gold price, exchange rates and stock price indices have been undertaken. Only a few studies haveexamined the relationship between crude oil price, gold price, exchange rates with stock


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market in general and Indian stock exchanges in particular. Based on very few studies inIndia, it is found that the impact of crude oil price rise, gold price rise and devaluation ofcurrencies in Indian stock market is unvoiced.

Objectives To study the trend of BSE-30 index using monthly data for the last 14 years. Determine a ARIMAX model to predict(forecast) the BSE index value. Test of Co-integration between BSE index, Oil prices and Gold prices. Test the causality between BSE Index, International crude oil prices and International

gold price.

Data Summary :

Variable Obs Mean Std. Dev. Min Max

BSE_Index 165 12413.8 6657.38 2811.6 26638.1

Oil Price ($/bbl) 165 69.6641 33.3948 18.71 132.72

Gold Price ($/oz) 165 856.987 482.132 260.5 1771.85

Tool Used :

Stata 12.0, Microsoft excel

Methodology

1. Analysis of Trends in BSE Index time seriesData for BSE Index (Monthly 2001-2014) shows an increasing trend over the given time periodas evident from scatter diagram and the line graph.


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2. Testing for stationarity of BSE index time seriesTest : Dickey Fuller Test

Hypothesis:

H0: BSE Index Series is Non-stationary

H1; BSE Index Series is Stationary.

Command: dfuller bse

Result:


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Inference:

As the p-value is greater than 0.05, so we do not reject the null hypothesis that BSE Index seriesis non stationary .

3. Differencing of BSE Index Series to make it stationaryUsing the method successive differencing to lessen the trend, starting from the first difference.

We now perform the first difference of the BSE series and test for stationary using dfuller test.

Command: gen d_bse= D.bse;

dfuller d_bse;

Result:

Inference:

As p-value is less than 0.05, we reject the null hypothesis that series is non-stationary. Hence, weconclude, BSE index is f ir st-order stationary seri es .


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Fig: First order BSE index series is stationary.

4. Determination of AR(p), I(d) and MA(q) term for ARIMAX model

For determining value of AR and MA terms , we will analyze the ACF and PACF correlogram.

Command: corrgram d_bse; ac d_bse ; pac d_bse

Result:


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As we can see, the ACF in the correlogram shows a declining trend from the first lag .So, we test for Moving Average order process of q=0,1.

Since the first difference of the series is stationary. It implies d= 1. After the first lag , the pacf lies within the 95% confidence interval. Hence, we test for p=1,0.

5. Selection of best ARIMAX model:

Iteration 1:Dependent Variable : BSE IndexIndependent Variables : Oil Price, Gold Pricep=1,d=1,q=1


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Iteration 2:Dependent Variable: BSE IndexIndependent Variables: Oil Pricep=1,d=1,q=1


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Iteration 3:Dependent Variable: BSE IndexIndependent Variables: Oil Price, Gold Pricep=0,d=1,q=0


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Iteration 4:Dependent Variable: BSE IndexIndependent Variables: Oil Pricep=0,d=1,q=0

Final Model:Based on Statistical significant independent variable and model with least value of AIC and BIC, our final model is the model in Iteration 4. Also the coefficient for Gold came out to beinsignificant, hence final model includes oil prices as independent variable.

ARIMAX(0,1,0)Independent variable : Oil PriceDependent Variable: BSE Index


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7. Test for autocorrelation: Durbin Watson test

We predict the residual and check for autocorrelation using Durbin Watson (DW) Test

Command : dwstat

Result:

Inference: As DW stat is close to 2, we can conclude there is no autocorrelation .

8. Test for White Noise

Hypothesis:

H0 : The residual data has white-noiseH1 : There is no white-noise in residual data

Commands: predict ehat,residualswntestb ehatwntestb ehat,table

Result:


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Inference: The White-Noise test gives a p-value of 0.9724 (> 0.05) , which is statistically

insignificant. So we do not reject the hypothesis that the variable has white-noise.

This means there is no auto correlation in the data and so it follows random walk andcan be used for forecasting using the appropriate ARIMA(0,1,0) model


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9.Prediction of Dependent Variable

Commands: predict p_bse, ytsline bse p_bse

Result


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10. Co-Integration AnalysisBSE Index, Oil price and Gold Price time series are all first order stationary, so we can check forco-integration among them:

10.1 Co-integration between BSE Index and Oil Prices

As p-value is less than 0.05, so we can reject the null hypothesis that there is no co-integration.Hence, we can conclude, Oil prices and BSE index are co-integrated.


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10.2 Co-integration between BSE Index and Gold Prices

As p-value is greater than 0.05, we fail to reject null hypothesis that there is no co-integration between Gold prices and BSE Index.


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11. Granger Causality Test

Commands:var bse oil goldvargranger

Result:

Inference

Di rect and reverse causality between BSE index and Oil prices is observed as p-value


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There is a direct and reverse causality between BSE index and international oil prices.capita. This could be due to the fact that with increase in GDP per capita in developedeconomy there can be better agricultural technique employed to increase the yield perhectare.

Terms And Terminologies1) Scatter diagram : A scatter diagram is a plot of X-Y data points on a two dimensional graph.

2) Autocorrelation : It is the correlation between a variable lagged one or two more periods and itself.

3) Autocorrelation Function : It is a graph of autocorrelations for various lags of a time series.

4) Stationary Series : A Stationary series is one whose basic statistical properties remains constant overtime.

5)Time Series : A time series is a data that are collected, recorded or observed over successiveincrements of time.

6) Mean Square Error : 1 (Yi - Yest )2

N7) Exponential Moving : It is a procedure for continually revising a forecast in the light of more recentexperiences.

8) Moving Average : A moving average of order k is the mean value of k consecutive observations.The most recent MA value provides a forecasting for the next period.

9) Simple Average : A simple average uses the mean of all relevant historical observations as theforecast for the next period.

10) Autoregressive Model : An Autoregressive model expresses a forecast as a function of previousvalues of a time series.

11) Co integrated Time series : A set of non-stationary time series for which simple differencingproduces a stationary series in each case is said to be cointegrated if and only if some linearcombination of the series is stationary.

12) Box-Jenkins Methodology : It refers to a set of procedure for identifying, fitting and checking ARIMAmodels with time series data.

13 ) Dickey-Fuller test : Test to test whether a unit root is present in autoregressive model.

14 ) Granger causality : To test for determining whether one time series is useful for forecasting another.

15) Vector Auto regression : Model to capture linear interdependecies among multiple time series.


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References :

http://www.stata.com/training/public/time-series-analysis-using-stata/

Applied Econometric Time Series - Walter Enders.

Identifying the numbers of AR or MA terms in an ARIMA model- www.duke.edu
http://www.stata.com/training/public/time-series-analysis-using-stata/http://www.stata.com/training/public/time-series-analysis-using-stata/http://www.duke.edu/http://www.duke.edu/http://www.duke.edu/http://www.duke.edu/http://www.stata.com/training/public/time-series-analysis-using-stata/

Time series Project Final

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