Forecasting Stock Prices and Portfolio Decisions using Time Series

I wish I had put more money into this stock. I should have trusted my technical analysis. I need to trust my broker. My gut feeling told me I should have cut my losses. Aren't these all statements that we have heard individuals involved in stock markets say at some point?

With a stock price, you can instantly see the impact of getting forecast right or wrong. It pays to be right. But if it were so simple, anyone could forecast the closing price of a blue-chip share and make millions. Maybe if it were so simple, there wouldn't be anything to distinguish investors, and the returns for everyone investing would be smaller, as the winning prize would be split across millions of investors. The ability to make the right call on investment decisions is what differentiates successful and unsuccessful investors...

Portfolio forecasting

The use of forecasting, and, in particular, using time series forecasting, goes beyond the scope of a few stocks. Hence, in this chapter, we will also cover the forecasting of portfolios. A portfolio can be defined as simply a range of investments held by a person or organization. An individual may have multiple stocks. Thus, the need to look at the scenarios where investment in a single stock needs to be assessed against holdings in other stocks. Certainly, there must also be other investment instruments that a person can hold. What about gold, bonds, real estate, and the now in vogue cryptocurrencies, such as Bitcoin?

Most organizations deal with multiple items in a portfolio. These items are usually spread across asset and liability classes. The portfolio usually isn't compiled in a day. It evolves over a period of time, and there are entrants and...

A portfolio demands decisions

A company that decides to invest all of its money in fixed deposits, rather than in government bonds, will have more decisions to make. At some point in time, the cash flow of the company will increase or decrease. If it increases, there might be further investment decisions, and a need to decide between various investment choices. Again, the easiest choice would be to go for the option that offers the highest rate of return. But what about putting all of your eggs in one basket? Shouldn't the company think about the need to diversify? Is the option of fixed deposits as attractive as last time? Interest rates might have moved, or the fixed term on offer could be different. And what about using the funds to expand, rather than investing? Suppose that this tranche of funds available for investment is expected to be invested for a longer time period...

Forecasting process

The forecasting process, illustrated in the following diagram, represents a typical process flow that can be applied to both time series and other models. There isn't a stage in the process that is more important than others. However, a good understanding of the business problem should be the building block of any modeling process:

Figure 2.2: Forecasting process

Let us walk through the process of forecasting:

Define the business problem and state what the model expects to achieve.
Collect data from various sources and systems and transform it to clean data.
Plot the data, run statistical tests, fit the model, and interpret the results.
Validate the model by using a holdout sample.
Obtain a model sign after it meets the technical and the business requirements. Integrate it into the business process.

Most modelers spend a disproportionate amount of time...

Visualization of time series data

With an increase in software, there is also the option to use fancy charts to visualize data, while creating a better understanding of the underlying story. However, some charts don't work as well with time series data. The line chart is the one that works best for almost all business cases. Let's explore the case of the growth over lending in the last three years:

Figure 2.3: Visualization of time series

All of the six charts are trying to tell the same story. The bank has seen lending grow from £2.35 billion to £2.84 billion between 2015 and 2017. However, some of the charts are much better placed to tell the story. The best placed is the line chart, which depicts the time on the x-axis and the value of lending on the y-axis. As we read the chart, it becomes apparent that the line shows a growth in lending. The bar chart...

Dealing with multicollinearity

The modeler still wasn't sure that the model was robust enough. He remembered that he hadn't tested the model for any effects of multicollinearity. We spoke briefly about this phenomenon when we studied the correlation of stock prices with each of the eight independent variables proposed for the regression model. The multicollinearity test was run using the tolerance and the variance inflation factor (VIF).

The PROC REG code for multicollinearity is as follows:

PROC REG DATA=build plots(only label)=(RStudentByLeverage CooksD); 
ID date; 
MODEL stock = basket_index -- m1_money_supply_index/tol vif; 
RUN;

Figure 2.18: Partial output for multicollinearity

The tolerance is computed as 1-R². When the R² is high, the tolerance value is very low. Such low values of tolerance are indicative of multicollinearity. The VIF is derived by taking the...

Role of autocorrelation

One of the assumptions for ordinary least squares regression is that the error terms are independent. However, with time series data, much of the time, the error terms are correlated. This is also known as autocorrelation. The regression tests performed up until now don't test for autocorrelation. If autocorrelation is present in the model, then the parameter estimates may not be accurate, and the standard error estimates will be biased.

While the AUTOREG procedure should ideally be used for regressing time series data, we can still try to evaluate the model for autocorrelation by using PROC REG, which was used earlier. The statistic that is going to help us explore the autocorrelation is the Durbin-Watson (DW) statistic.

The PROC REG code for autocorrelation is as follows:

PROC REG DATA=build; 
ID date; 
MODEL basket_index eps p_e_ratio global_mkt_share...

Scoring based on PROC REG

Once we have built the regression model, we need to generate scores for a holdout sample. The holdout sample contains one month of observed data. At times, when building the model, we over fit the data. It is always a good idea to have a holdout sample on which the model can be fitted. There isn't anything better than using the observed values to see how well the predictions were made. The holdout sample shouldn't be too short or too future looking when compared to what has been built into the model.

We cannot expect the model that we have built for daily stock prices using almost three years of data to help us predict three years ahead. Also, using our model to predict just one day ahead and using that as a holdout sample would be too lenient on the model, and would not check for its practical use with a decent data size.

We will write the...

Recap of key terms

Some of the terms that we used in this chapter are:

ARIMA: The ARIMA model was analyzed by looking at various aspects of the model. We gained an understanding of the auto-regressive and moving average component of ARIMA. We also looked at the p, d, and q elements of the model. We developed an understanding of how the process helps to deal with autocorrelation, in comparison to regression. We forecasted values from the model using the historical data from the variable of interest only.
Dependent: The variable that we are trying to forecast or gain a better understanding of is the dependent. We can use a series of independent variables to try and forecast a dependent variable.
Differencing: This is the transformation of the data that we have used to derive a new variable, based on the change of the series from one data point to another.
Independent: The variables...

Summary

In this chapter, we explored aspects of portfolio forecasting, steps in the forecasting process, tips for the visualization of time series data, and model building for a business case. Both regression and ARIMA models were used, and we compared the results of the model by using a validation sample. In the next chapter, we will discuss risk modeling.