Gulati SAS for Finance

Forecasting and data analysis techniques with real-world examples to build powerful financial models
1. Auflage 2024
ISBN: 978-1-78862-248-6
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 306 Seiten

SAS is a groundbreaking tool for advanced predictive and statistical analytics used by top banks and financial corporations to establish insights from their financial data.

SAS for Finance offers you the opportunity to leverage the power of SAS analytics in redefining your data. Packed with real-world examples from leading financial institutions, the author discusses statistical models using time series data to resolve business issues.

This book shows you how to exploit the capabilities of this high-powered package to create clean, accurate financial models. You can easily assess the pros and cons of models to suit your unique business needs.

By the end of this book, you will be able to leverage the true power of SAS to design and develop accurate analytical models to gain deeper insights into your financial data.

Autoren/Hrsg.

Gulati, Harish

Fachgebiete

• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Automatische Datenerfassung, Datenanalyse
• Mathematik | Informatik EDV | Informatik Digital Lifestyle Online Banking & Finance
• Mathematik | Informatik EDV | Informatik Informatik Mensch-Maschine-Interaktion Informationsarchitektur
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Datenbankdesign & Datenbanktheorie

Inhaltsverzeichnis

Table of Contents - Introduction to Time Series modelling in financial industry
- Forecasting stock prices and portfolio decisions using Time Series data (Stocks Forecasting)
- Build Probability of Default (PD) model to adhere to BASEL norms (Risk Management)
- Revenue forecasting to manage budgets/operational strategies (Budget and Demand Forecasting)
- Inflation forecasting for financial planning (Econometric Modelling)

- Manage customer loyalty using Time Series data (Customer Loyalty)
- Pattern Discovery in Product Purchases (Segmentation)

Leseproben

ARIMA

ARIMA models are also referred to as Box-Jenkins models, owing to the approach made popular by the statisticians George Box and Gwilym Jenkins. It is worth noting that along with ARIMA, there are other terms, such as AR, MA, and ARMA, which help to form the ARIMA approach. and are remembered for their contributions, as they bought together the AR and the MA approach. The ARIMA approach was developed in three parts. Let's first explore why ARIMA is relevant to time series forecasting. We can then focus on understanding the nuances of ARIMA.

One of the reasons we want to use ARIMA is to compare our multivariate model to a different methodology. We do occasionally see multivariate regression used for forecasting in the financial world, but most people prefer to use ARIMA. When we want to forecast something, we need to know what is influencing or driving the behavior of the variable we want to forecast. On a lot of occasions, we don't know what is driving the behavior. Yes, we can attempt to gather hundreds of independent variables and try to make our variable of interest as the dependent variable, and we can try to generate a regression model to identify drivers, get the parameter estimates, and create an equation for forecasting the dependent variable. But collecting, storing, and analyzing these independent variables takes time. Also, we are limited by the number and nature of variables we select.

At times, some users of the models may feel that the right influencing factors were never assessed, as they weren't part of the independent variables tested for their significance in forecasting. Stock prices are a perfect example of people having differing views on what influences them. Someone will point out that the financial ratios are important, others will talk about the recommendations from brokers, some will mention the global factors, and others will talk about their gut feelings. There is a cost associated with testing all of these potential influencers.

Moreover, the multivariate regression methodology doesn't incorporate any learnings from the residual errors generated during the forecasting process. The ARIMA models use information from past data points and the residuals generated. We can still use independent variables to generate forecasts in ARIMA, but these so-called independent variables in the ARIMA context may just be transformations of the variable (or, in this case, the dependent) of interest. The equation of such a model could be, simply, . The term is an independent variable in some sense, but it is merely a transformation of the dependent variable. Due to this particular way of using independent variables, this type of analysis is also called a univariate analysis. In our business problem, we are only concerned about the variable stock.

Let's run our first ARIMA model code:

PROC ARIMA code:

PROC ARIMA Data=build; IDENTIFY VAR=STOCK; RUN;

shows the autocorrelation test at various lags. By default, the first lag that is shown in the output is lag 6:

Figure 2.21.1: PROC ARIMA output - autocorrelation

Notice that the code statement only had a single variable of interest. This is different from the REG procedure, to begin with. Later on, we will try to explore the effect of other variables on our main variable of interest, stock.

We didn't act on the autocorrelation that we found in the multivariate regression model. It's now time to explore the autocorrelation using the ACF, or the autocovariance plot. The -axis plots the lag, and the -axis, the autocovariance level. The lag is simply the time between the observations. As we can see, in this case, the reduction in autocovariance is a smooth process.

The reduction is happening at a constant, but a, gradual pace. Although this makes the graph look symmetric, it is an indication of an issue that creeps into time series data. The issue, in this case, is called non-stationarity. We want our autocorrelations to exhibit stationarity:

Figure 2.21.2: PROC ARIMA output - trend and correlation

When we spoke about multivariate regression, we explored the role of the constant value in a regression equation. Time series has two components: the deterministic aspect and the stochastic aspect. The stochastic aspect, in theory, is loosely related to the role of the constant in the regression. The non-error part, which explains the relationship of the dependent with the independent variables (a lagged form of dependent, or some other transformation, in the case of time series), is the deterministic aspect. It is something that, in plain language, we can determine by assigning a weight or parameter value to the independent variable, whereas the error of the equation is the stochastic part that explains the time series.

The stochastic part relates to the random error in forecasting. This random error captures the autocorrelation between two lags of the time series. For instance, the stock price is $5 today, and there is more of a likelihood that it will be $5 or +- 0.1 in a world with slow-moving factors. Hence, today's stock price is more likely to be related to yesterday's, and maybe even the day of the stock price recorded a week ago. This is a non-stationary process. A stationary process can be defined as one where the mean, variance, and autocorrelation don't change over time.

So, why is stationarity important? With stationarity, we have no trend, as the mean doesn't vary over time. The variance is constant, rather than fluctuating all over. The autocovariance depends only on a lag of, let's say, the most recent period. In our case, we can say that with a stationarity series, the autocovariance is only dependent on yesterday's closing stock price. Having a stationarity series makes forecasting more robust.

In our stock price example, a non-stationary series is being observed, due to the following reasons:

• The trend of the stock price is generally increasing since the start of the data period. This is clearly demonstrated by the output of PROC ARIMA in the plot where the -axis charts the observation number, and the -axis, the price of the stock.
• Variance is changing, and we have observed this in the residual charts that were produced as part of PROC REG.

There are probably seasonal effects, relating to the product launches or the Christmas time period. Just prior to the holiday season, the mobile manufacturer in question is launching new handsets. This could surely have a seasonal effect on the data. Again, the seasonal jumps we are referring to are probably the two spikes in the PROC ARIMA plot that we can observe. Overall, the trend is of a rising stock price, and there are two major jumps in the time series across the almost three years of data we have.

To make the series stationary, we could either difference it (the most popular method), try some log transformations (the second most popular approach in the industry), or use moving averages, based on some sort of judgment. Differencing tends to be the most popular option, as, from a practical consideration, it is an easier method to deploy. If, let's say, the first order differencing doesn't work, you can specify higher orders. But what is differencing?

Differencing is simply, .

Let's try to difference our data and observe the change in the ACF distribution.

The PROC ARIMA code for first order differencing is as follows:

PROC ARIMA Data=build; IDENTIFY VAR=STOCK(1); RUN;

Figure 2.22.1: First order differencing - autocorrelation

Figure 2.22.2: First order differencing - trend and correlation

So, what happened to the gradually declining autocovariance observed in the last run of PROC ARIMA? Well, the differencing has had its effect, and now, after the second lag, we can see that the series dramatically declines. We now have a stationary series, just by doing the first order differencing. Note that the only change in the two PROC ARIMA statements that we have seen until now is the addition of the syntax (1) in the code for differencing.

Also, notice the observation versus the stock (1) plot. Remember, without the differencing, we had a trend. It has now disappeared after the differencing. We no longer have seasonality in the chart. We do have some points where the variation is larger than most of the points. A large majority of the points have a variance close to zero. Hence, by looking at the plot, we can see that differencing seems to be delivering the required results.

Before exploring the partial autocorrelation function graph, let's spare some moments for the white noise table summary produced. Note the difference between the white noise summaries with and without differencing. Prior to differencing, for all of the four lags exhibited, we had a small -value.

After differencing, lags 6 and 12 still have a small -value. For lag 18, the -value is not significant, but again, for lag 24, the lag value is significant. Remember that we are more concerned about the second lag after differencing, as this is when the autocovariance suddenly declines. Since the -value at lag 2 after differencing is significant, we can state that there is no white noise; that is, at least some of the autocorrelations up to lag 2 are not zero. If the autocorrelation at all lags is zero, and we determine that there is white noise, then there is no point to model ahead. Remember that we aren't using a multivariate approach to use a lot of...

Über Autor(innen)

Gulati Harish :

Harish Gulati is a consultant, analyst, modeler, and trainer based in London. He has 16 years of financial, consulting, and project management experience across leading banks, management consultancies, and media hubs. He enjoys demystifying his complex line of work in his spare time. This has led him to be an author and orator at analytical forums. His published books include SAS for Finance by Packt and Role of a Data Analyst, published by the British Chartered Institute of IT (BCS). He has an MBA in brand communications and a degree in psychology.