INTRODUCTION:
A bubble is a term which has been invented in financial dictionary when there is a rapid increase or decrease in the price of the assets, due to mathematical estimations in a very short duration of time and finally deflates after sometime.The reason behind this sudden outburst in asset prices can be explained by one of the key concept of behavioural finance which is known as the Herd Behaviour of the market.
Due to this behaviour at the time of loss, the economic cost shoots up rapidly as it puts a structural breakdown in the time series because of which these are also called “market destabilizers”. This is basically of three types. The first is Information based which happens when everyone responds in a similar manner after hearing the announced information from the sources.
The second type is Reputation based which arises when a big trading house is looking to go for a particular trading stance. The third is Compensation based which occurs when big institutional managers are keen on taking the profits in the interest of protecting the fund earnings before the end of the year.
Behavioural Finance explains two very important concepts which are related to the formation as well pop of the bubble. This behaviour leads the group of people to go for either financial pandits or some renowned fund manager which shows their overconfidence and not calculative decision making. This leads to irrationality, distortion and incorrect judgements resulting in cognitive biasness.
These explain the situation very well and based on them future predictions can be made which could save the public money that is coming in and going outof the financial market during the crucial time. In this study we will also try to understand the relationship between Bubble testing and Gini Coefficient. Gini index is nothing but a deviation measure from perfect equal distribution of resources and expenditure within an economy. The higher the coefficient it indicates that economy is moving towards inequality and lower index indicates that the economy is moving towards perfect equality.
LITERATURE REVIEW:
Bubble Testing is not a new phenomenon. It has it traces from centuries. The later part of 20th century has seen the traces of the Dutch Tulip Bubble. Various researches in the past are been done on bubble testing and has found traces in a stochastic time series with a drift.
A study in this context was done byFama(1965) in which he stated that as per efficient market hypothesis, there is nothing like bubble and he claimed that bubble cannot exist in a time series. But a lot of study in this field during the past four decades has found and reported events while spotting the bubble in time series which have proved his claim as erroneous. Much before Fama, Keynes (1936) has prognosticated and provided a rational for the existence of bubble in a time series.
Another study by Evan (1991) talks about the theory of periodically collapsing bubble. Brunnermeier andAbreu (2003) in his study argued that bubbles transpire not because of irrationality in stock market, they occur because of wrong pricing of assets. A lot of studies are done on bubble testing by various researchers but none of their studies have scrutinized the reason for bubble formation in the market and how its presence can be felt by everyone in the market. Jarrow, Protter and Shimbo (2007) in their study stated that bubble can be deducted with the help of derivatives against the underlying assets. A major arrear in their claim was that their research has its strict boundaries and there was a shortfall of empirical evidence supporting their claim.
The first bubble test was conducted and constructed by Shiller and Leroy and porter (1981) known as “Variable Bound Test”, a test to predict the rational value of stock based on the present value of dividends that are paid already to the shareholders. If the rational price is less than the actual price then the presence of bubble can be indicated. Some of the criticism was shown by some researchers on this test.
Flavin (1983) and Kleidon (1986) criticized the test stating that it is terminal value bias and small sample bias which affects the reliability of the study. Diba and Grossman (1988) came up with another tool i.e. stationarity for detecting bubble. This test was based on some unobserved variables and future value. Although this study was criticized by Gurkaynak (2008) but still it was clearly evident that their work has given accurate results for a long set of time series data. Gurkaynak (2008) mentioned two gaps related to the study said. Firstis non-stationarity cannot be detected even when it is present with a great degree of certainty and another is that only past dividends are taken into consideration. Various studies were done using various tools to predict bubble. One such study was conducted by West (1987) in which he came up with the equation of ARIMA.Froot and Ostfeld’s (1991) in their study differentiated between intrinsic and rational bubble; they again used dividend payments as a tool. Gurkaynak (2008) mentioned in his study that model should ideally be linear but if we consider log dividend, as a outcome of it model will come out as non-linear. Ma and Kanas (2004) has used this model over a century for a long data set of capital market and constituted it as a better model for forecasting with accuracy. Van Norden and Vigfusson (1998) with the help of switch regression apprehended bubble from the fundamental value to as more of a variable value.
A unique study was conducted by Hall and Sola (1993). They introduced the check of stationarity with the use of extended Augmented Dickey Fuller Test to check whether the time series is following stationarity or tending towards anexplosive pattern. However, this test failed in the short run just like any other tests in the domain of a bubble. Phillips, Wu and Yu (2011) introduced Supremum ADF or SADP test for identifying bubble quite effectively. This study was further extended by Phillips, Shi, and Yu (2013) and they came out with the use of generalized SADF for the prediction of bubble efficiently. However, in the same direction Taipalus (2012) used ADF i.e. (traditional Unit Root Test), RADF via Monte Carlo simulation in his study on US stock market data, where he found traces of bubble coming up well before 12 months. Sornett et al (2010) came up with the Log-periodic power law (LPPL) tool to look into two collapses that happened in the Chinese Stock Exchange market indexed i.e. (SSEC; SSZE).
He tried to merge the conventional rational theory of finance with the behavioural theory. However, Sornette and Zhou (2006) modified this LPPL tool to incorporate fundamental economic factors (like spread, exchange rates, interest rates and historical volatility), participating as a proof of herding. Both Katja Taipalus model and Hall and Sola model was extended by Caspi (2013).
He used Rolling window ADF, Standard ADF, Supremum SADF and generalized SADF (GSADF) where rejection of null hypothesis in every case created the empirical proof of existence of Bubble. Similarly, Korkos (2014) has used RADF and GSADF tools to test in US capital market and detected the trace of bubble. Ghosh, Bikramaditya (2016) conducted a similar study and extend it to do an in-depth analysisof CNX-Nifty. He conducted this test using four tools i.e. ADF, RADF, SADF and GSADF. Result of this test fails to reject null hypothesis indicating that there is a presence of asset price bubble in CNX-Nifty.
RESEARCH METHODOLOGY:
The equation that is used in this study is
Y(t) is monthly closing of crude oil production,
μ is the intercept, p is the maximum number of lags, 
is the
differentiated lag coefficient for “i” lags and 
is the error
term. Four tests i.e. the variations of Augmented Dickey Fuller Test for
stationarity have been conducted on Crude oil production closing between 31st January 1998 and 28th
February 2017. Total number of observations is 230. RADF test is a rolling
regression test which is prepared on subsequent sub-samples of the main sample
with the rolling forward initialization. Each sub-sample is fixed and finite.
Moreover, bubble detection is dependent on this fact, therefore the accuracy of
prediction is dependent upon the optimum size of sub-sample. In this study,
each sub-sample is fixed at. Both SADF and GSADF are recursive. It implies that
solution of a bigger problem lies in the solution of smaller problems that
constitutes the bigger problem. SADF test has a factor “Supremum” that is the
least upper bound in a partially ordered set i.e. from mathematical concepts.
GSADF test has been constructed by Phillips, Shi and Yu (2012). This test
observes the periodically collapsing bubbles, using a non-static and dynamic
window, in place of fixed window as in SADF. This helps in avoiding being
sensitive to sample start data.
Hypothesis Setting:
H0: δ=1 Ha: δ >1. So, the H0 confirms that the linear stochastic time series has unit root, so it is non-stationary in nature and the Ha confirms that the time series is stationary in nature, in fact it is said to have a mildly explosive autoregressive coefficient. So, if the P value is lower than 5%, H0 is rejected and thus the evidence of a price bubble will be evident. On the contrary if the P value is higher than 5%, then H0 is accepted thus evidence of price bubble is termed to be absent.