INTRODUCTION:
BERXIT is the withdrawal of UK from European Union which would pose an impact on the structures of power and administration of both UK and EU. The economies of UK and other nations also are claimed to have affected by the event. There were many discussions on the immediate impact of BREXIT on the various aspects. The present study is an attempt to understand and quantify the effect of this event on the stock market of three major economies of the world- US, UK and India. The objective of the analysis is to trace the effect from the very next day of the intervention.
REVIEW OF LITERATURE:
Intervention analysis is prominently used to assess the impact of an event or incident on a time series. Tsay[1] proposed intervention ARIMA model. ARIMA intervention models are successfully implemented in various circumstances where there is a shift from the existing trend or pattern. Sridharan et al[2] have analysed the deterrent impact of parole abolition and sentence reform by Virginia’s legislature using different methods of intervention analysis. The study consists of a simple regression models, ARIMA intervention model and structural time series STS models. ARIMA and STS models are found to include trend, seasonality and random effects
Roy et al[3] have developed an intervention ARIMA model to explain and analyse the effect of the financial tsunami that affected global finance in 2008 in Chinese manufacturing industry. The study develops a model to find the temporary but immediate and abrupt effect of the crisis. A comparative analysis of ARIMA to Intervention compares the results of the ARIMA and ARIMA Intervention models, confirming that the application of intervention analysis is appropriate for explaining the dynamics and impact of interruptions and changes of time-series in a more detailed and precise manner.
Forecasting the Incoming calls to a telemarketing centers is analyzed by Bianchi[4] is done by Holt–Winters (HW) exponentially weighted moving average models and is compared with Box–Jenkins (ARIMA) modeling with intervention analysis. The study concludes that Intervention included in ARIMA is giving a better model than simple models. The effect of introduction on certain policies on import of gold in India is analysed[5] where the intervention ARIMA model is developed which reveals the significant dip in the import of gold that can be attributed to the policies.
Intervention analysis is used [6] to evaluate three antiterrorist policies viz, increased airport security screening, and increased securities at US embassies and institution of UN convention to prevent crimes against diplomatic persons. The study analyses whether the crackdown of one particular mode of attack has a substitution effect. Furthermore the study also tests the magnitude and the dynamic realization of the substitution effect.
The effect of BREXIT is analyzed by few researchers from various dimensions. FICCI [7] brings out this unprecedented global development as a grim economic situation which would take two to three years to recover. This might also lead UK to a recession. The analysis suggests that the investment also might be impacted as the uncertainty may reduce the confidence level of potential investors.
The report[8] to discuss the impact of BREXIT on British economy brings out the concerns on all important elements like immigration, trade and manufacturing, financial services, regulations, innovations and productivity, consumption and property market and more. It is assumed that Britain’s economic prospects would remain good even if it is outside EU.
METHODOLOGY:
ARIMA MODEL:
The ARIMA (p,d,q) model[9] of a time series refers to the model which is stationary at level with p autoregressive terms and q moving average terms. It may be denoted by
Φ(B) (1 – B)dyt= θ(B)εt
Where Φ(B) = 1 – Φ1B – Φ2B2 ..... ΦpBp (Autoregressive parameter) (i)
θ(B) = 1 – θ 1B – θ2B2 ..... θqBq (Moving Average parameter) (ii)
εt – is the noise term and B is the backshift operator.
ARIMA model is developed in three steps: model identification, parameter estimation and diagnostic checking. Initial plotting of correlogram helps us in tentative selection of the parameters. Estimation is carried out by method of iterative least squares. The least values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) are considered for deciding the best model where.
AIC= Tlogσ2 + 2(p + q+ 1) (iii)
BIC = Tlogσ2 + 2(p + q+ 1) log T (iv)
Where p and q are the parameters of ARIMA model, σ is the standard deviation of the model and T is the number of observations used in estimating the model.
ARIMA MODEL WITH INTERVENTION:
The ARIMA model with intervention suggested by Box and Tiao[10] is widely used to analyse the impact of external events on time dependent variables. The methodology of intervention analysis is
i) Develop a model for the time series before intervention
ii) Add one or more dummy variables that represent the timing of the intervention
iii) Re-estimate the model, including the new dummy variables for the entire series
iv) Interpret the coefficients of the dummy variables as measures of the effect of the intervention
The intervention model has two components- the noise component which represents the pre-intervention period and the intervention component that incorporates the effect of the intervention in the model. It may be represented as
Yt
= 
bIt
+ 
t (v)
where Yt is the response series, I is the indicator variable coded as a binomial variable with values 0and 1to identify the intervention period, ω(B) the slope parameter, δ(B) the impact parameter, ϕ(B)the autoregressive parameter, θ(B) the moving average parameter and B the backshift operator. The forecasting performance of this model can be assessed by the values of Mean Square Error (MSE), Root Mean square Error (RMSE) and Mean Absolute Percent Error (MAPE) value which are supposed to be as less as possible.
DATA:
The data used in the study includes pre and post stock indices of three economies- US, UK and India. The daily index of SandP, FTSE and NIFTY are collected from June 23rd 2015 to June 23rd 2016as pre- intervention period and from June 24th 2016 to November 23rd 2016 as post-intervention period.
RESULTS AND DISCUSSION:
A descriptive analysis of the three indices is carried out. Box-plots of three sets of indices presented in Figure 1 and the descriptive analysis of the indices is presented in Table 1 to explore their performance.
Figure 1. Box-plot of the three indices
Table 1: Descriptive statistics of the pre and post Brexit data
|
|
FTSE-UK |
SandP-US |
NIFTY-India |
Full data |
|||||
|
Pre-BREXIT |
Post-BREXIT |
Pre-BREXIT |
Post-BREXIT |
Pre-BREXIT |
Post-BREXIT |
UK |
US |
India |
|
|
Average |
6230.06 |
6794.57 |
2028.48 |
2153.91 |
7898.002 |
8547.71 |
6403.4 |
2066.63 |
8093.84 |
|
SD |
251.833 |
181.78 |
72.58 |
35.7589 |
384.54 |
233.707 |
349.24 |
85.94 |
456.79 |
|
Skewness |
0.3025 |
-1.6231 |
-0.8392 |
-1.5622 |
-0.1416 |
-0.94 |
0.098 |
-0.62 |
2.249 |
|
Kurtosis |
3.0527 |
7.7384 |
2.5752 |
6.4668 |
2.5773 |
3.1532 |
1.96 |
2.71 |
2.249 |
|
Jarque-Bera |
3.9196 (0.141) |
155.3* (0.00) |
31.717* (0.00) |
100.73* (0.00) |
2.6746 (0.2625) |
15.86* (0.00) |
17.17* (0.09) |
25.16 (0.00) |
12.26* (0.002) |
|
N |
255 |
113 |
254 |
111 |
248 |
107 |
368 |
365 |
355 |