This presentation shows how the prices of stock changes dynamically.

1. Dynamic Pricing of Stocks
A Game Theoretic Approach

2. Previous Work Done
 Optimal Pricing
 Supply Chain Model
 Nash Equilibrium in Spot Pricing
 Prisoner’s Dilemma approach in Stock Market scenario

3.  Pn: Price of stock after n time intervals
 P0: Present price of stock
 r: Rate of return
 DIVi: Dividend after ith time interval
 P0 = (P1+DIV1)/(1+r) -(1)

7. TIME SERIES ANALYSIS
 What is Time Series Analysis?
Time series analysis comprises methods for analyzing time series data in order
to extract meaningful statistics and other characteristics of data.
Time series forecasting is the use of a model to predict future values based on
previously observed values.

8. Types of data
 Seasonal data:
It comprises of trend component, seasonal component and an irregular
component.
 Non-seasonal data:
It comprises of trend component and an irregular component.

9. Exponential Smoothing Method
 Exponential smoothing methods are useful for making forecasts, and make
no assumptions about the correlations between successive values of the
time series.
 However, if you want to make prediction intervals for forecasts made using
exponential smoothing methods, the prediction intervals require that the
forecast errors are uncorrelated and are normally distributed with mean
zero and constant variance.

10. ARIMA MODEL
 Autoregressive Integrated Moving Average (ARIMA) models include an
explicit statistical model for the irregular component of a time series, that
allows for non-zero autocorrelations in the irregular component.

11. Differencing a Time Series
 ARIMA models are defined for stationary time series.
 If we start off with a non-stationary time series, we first need to ‘difference’
the time series until we obtain a stationary time series.
 If we have to difference the time series d times to obtain a stationary series,
then we have an ARIMA(p,d,q) model, where d is the order of differencing
used.

12. Selecting a Candidate ARIMA Model
 Now to select the appropriate ARIMA model, find the values of most
appropriate values of p and q for an ARIMA(p,d,q) model.
 We usually need to examine the correlogram and partial correlogram of
the stationary time series.

13. Example
 We have used the prices of stocks of a company by considering interval of
42 sec.
 The plot of variation is as follows:

14. Differencing the time series
 In order to make the time series stationary, we difference the time series
once.
 The plot after differencing time series by 1 is:

15. Selecting the ARMA model
 The next step is to select the p,q values for arma model.
 For that we plot the correlogram and partial Correlogram
 The plot are as follows:

16. Forecasting
 Based on the plots we find out that the most preferable model involves
value of p as 0 and value of q as 1
 Preferable model can also be found out using the inbuilt function
auto.arima()

17. Plot for forecasting

18. Future Work
 We will try to implement this ARIMA MODEL on real time data of different
companies.
 We will try to improvise the arima model
 We will be focusing on prediction of stock price using artificial neural
network

19. Conclusion
 We tried to forecast future stock price using arma model.
 ARMA model is the most efficient model for predicting the stock prices.