QBUS2810: Statistical Modelling for Business Semester 1, 2022 Week 3 Tutorial
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QBUS2810: STATIsTIcAL MoDELLINc FoR BUsINEss
SEMEsTER 1, 2022
Week 3 Tutorial
The purpose of this tutorial is to give you some practice on the concepts, theory and application of simple linear regression and ordinary least squares estimation: assessing relationships between numerical (ratio) variables.
Business Problem
Financial economists and quantitative analysts are often searching for factors to help explain stock market price movements, i.e. financial returns. One popular theory is that of market spill-over effects, where price movements in one market influence price movements in other markets. We examine such spill-over effects between the US and Australian stock markets as a whole, using a simple linear regression model.
The data consist of daily percentage log-returns on each market, only for the days that both markets traded, as measured by the All Ordinaries (AORD) index on the ASX and the Standard and Poors 500 (S&P500) index on the US market. The data were collected from Yahoo Finance, and are in the files ”AORD Daily Jan2000 Feb2017 yahoo.csv” and ”SP500 Daily Jan2000 Feb2017 yahoo.csv”, in the same format they were deliv- ered in (including reverse time order).
There are seven columns in each file:
1. ’Date’: the date the row of data correspond to;
2. ’Open’: the opening value of the index on that date;
3. ’High’: the highest index value during that day;
4. ’Low’: the lowest index value during that day;
5. ’Close’: the recorded closing value of the index that day;
6. ’Volume’: the number of shares traded on the market that day;
7. ’Adj Close’: the adjusted closing value of the index that day;
The percentage log-returns for each market index are formed as follows:
Pt
rt = 100 x (log Pt - log Pt − l ) = 100 x log
starting at day 2 of each sample, using as Pt the column labelled ”Adj Close”, which is the adjusted closing price for each day and considered more accurate than ’Close’ (mostly they are the same in value).
In this tutorial, our goal is to analyse this data and assess whether or not there is a spill-over effect from the US market to the Australian market.
The data from Yahoo are in reverse time order. We first need to sort them into actual time order, using the ”sort values()” command in the Python file ”Tut3 code 2022.py”. Then:
(a) Plot the two indices over time and comment on their behavior.
(b) Form the two series of daily percentage log-returns and plot them over time. Comment on their behavior.
(c) Form histograms of each percentage log-return series, taking note that there are missing values in the data. Comment on these plots.
(d) The data need some more preparation prior to a regression analysis. Using the code provided, merge the two datasets on the date variable, and create a new data frame that has only one date variable, plus the SP500 and AORD returns on those dates, and finally a 3rd variable that is the SP500 return, on the day previous (called lag 1 or lagged) to that in the same row of the ’Date’ column. Conduct an exploratory analysis on the relationship between the AORD and SP500 returns on the same calendar day. Comment on this.
(e) A financial analyst points out that Australian time is ahead of US time, so that the return on day t in Australia becomes known well into the trading day t in the US. Thus, it makes little sense to think of either USt or AUt as an explanatory variable in a regression model for the other one. However, at the start of trading in Australia on day t, the result of US on day t - 1 has just become available. Australian traders literally awake to the news from the US market (day t - 1) each day. Conduct an exploratory analysis on the relationship between the AORD on day t and the SP500 index on day t - 1. Comment on this, including whether a linear model may be an appropriate choice.
(f) Fit a simple linear regression model to the data in part (e). Justify your choice of standard errors. Interpret and comment on the estimated relationship and model parameters.
(g) Is the model a strong fit to the data? Discuss.
(h) Is the model a good fit to the data? Are the LSA satisfied? Could/should we do anything to help improve the i.i.d assumption?
(i) Write a brief report summarising your findings about the spill-over relationship between the US and Australian markets.
2022-03-28