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July – December 2018

Using an intervention approach to analyse the 2008 US financial crisis

2008 US financial crisis

Katleho Makatjane, Edward Molefe and Roscoe van Wyk

  • OCT 2018
  • Tags Features, Finance
16 minutes to read


Katleho Makatjane, Edward Molefe and Roscoe van Wyk

How did the 2008 US financial crisis impact the real exchange rate in SA?

This study investigated the impact of the 2008 United States financial crisis on the real exchange rate in South Africa. The data used in this empirical analysis covers the period from January 2000 to June 2017. The seasonal autoregressive integrated moving average (SARIMA) intervention charter was used to carry out the analysis.

Where did this all start?

The 2007-2008 worldwide financial crisis was an astonishing and multifaceted process. The financial crisis came as a result of surplus liquidity as the Federal Reserve Chairman Ben Bernanke had excess savings that were used in global financial markets and US mortgage markets. In addition, insufficient assets and liability and the risk management practices of financial organisations resulted in the advancement of the 2007-2008 financial crisis. The crisis had spill-overs that affected various areas of the economy – such as financial markets and commodity markets.

Researchers have shown that from 2007 to 2008, the US national government initiated endeavours to avoid disturbing mortgage markets. That is why the crisis went through five stages:

  • Stage 1: The US experienced a housing bubble boosted by significant mortgage lending.
  • Stage 2: Other types of assets were also impacted by the crisis. This stage also impacted mortgage companies, investment banks and other banks worldwide.
  • Stage 3: This stage was characterised by the colossal addendum of liabilities from exposed banks which prompted the international liquidity crisis. This triggered anxiety about possible credit contagion of the same risk on the universal scale.
  • Stage 4: This stage was characterised by the disintegration of investment product structures which eliminated the comprehensive liquidity provisions into an article of trade, causing the bubble effect in this area.
  • Stage 5: A peak was reached in September 2008 with a massive shifting of funds into risk-free securities. Lehman Brothers filed for bankruptcy protection and the US investment banking system faced its ultimate demise.

The 2007-2008 financial crisis affected economies all over the world. Most economies started to recognise the effect of this crisis in March 2008.

The 2007-2008 financial crisis affected economies all over the world. Most economies started to recognise the effect of this crisis in March 2008. Therefore, the rationale of this study was to evaluate whether the 2007-2008 financial crisis had a transitory or long-term effect on the South African economy utilising the SARIMA intervention procedure. This intervention model is used to assess the patterns and duration of the financial crisis on the real exchange rate of South Africa. The study also wanted to assess whether the crisis had a transitory or permanent effect on the country’s economy. The empirical analysis used in this study is divided into three stages:

  • Firstly, the SARIMA model was used as benchmark to describe South Africa’s exchange rate.
  • Secondly, an intervention analysis was performed to appraise the effects of the 2008 financial crisis. This will assist the Monetary Policy Committee of South Africa to understand the linear co-movement of the country’s exchange rate.

Thirdly, a comparative analysis was done to determine whether the intervention analysis successfully represents the waves of 2008 financial crisis contrasted with SARIMA.

What other research has been done in this field?

The structural breaks in the data can be examined exogenously by assessing their impact with an ARIMA model that is developed on the basis of a time series. The difference between the actual data and the data without the bearing is known as the degree of the power of an exogenous event.

The number of data fluctuations that is more than or less than expected is based on the data trends before the intervention event.

The intervention is therefore used to determine the statistical influence of an exogenous intervention on a given time series and to measure the magnitude of the impact, if any.

Various researchers have used the intervention model to analyse time series prone to structural breaks. This includes Coshall (2003) who examined the impact of the September 11 terrorist attacks on international travel flows. Lai and Lu (2005) quantified the decline in the demand of air transport passengers in the US after the terrorists attack on September 11. Eisendrath and his co-researchers (2008) measured the waves of the September 11 terrorist attack on the Las Vegas Strip’s gaming volumes. Min and his co-researchers (2011) used an intervention model to analyse the consequence of Severe Acute Respiratory Syndrome (SARS) on Japanese demand for travel to Taiwan. Zheng and his co-researchers (2013) examined the impact of the 2007 recession on US restaurant stocks by employing an intervention model.

The SARIMA model with the intervention was also used by Ebhuoma, Gebreslasie and Magubane (2017) to model the outcome of the re-introduction of dichlorodiphenyltrichloroethane (DDT) on confirmed monthly malaria cases in KwaZulu-Natal. Results revealed both a sudden and a perpetual monthly decline in malaria. The cause of this decline was the aftermath of implementing an intervention policy to curb malaria. The long period of low malaria cases shows that the continued use of DDT did not act as an insect repellent as predicted. Therefore, the feasibility of reducing malaria transmission to zero in KwaZulu-Natal requires other reliable and complementary resources.

The study also wanted to assess whether the crisis had a transitory or permanent effect on the country’s economy

How was the study conducted?

Two models were proposed for this study, namely the SARIMA intervention model and SARIMA model. The SARIMA model served as benchmark model to show that the multiplicative SARIMA model denoted by SARIMA follows a certain mathematical form.

There should be no common factors between the seasonal autoregressive (SAR) polynomials and seasonal moving average (SMA). Also, SAR polynomials should correspond with the characteristic equation of SARMA because that is the role of the SAR model.

Because the 2008 financial crisis was unique, the intervention variable Zt symbolised some discrete event in which Zt=1 denotes the international financial crisis while Zt=0 denotes otherwise.

How the SARIMA model was developed

The SARIMA model was developed in three stages:

Step 1: The unit root test and the identification of the order of difference help to reduce the variance of the data and make the time series ready to be modelled by a stationary S (ARIMA) model. The Augmented Dickey-Fuller (ADF) test is usually applied for the unit root test. For model selection, the Akaike information criterion (AIC) and Schwartz Bayesian criterion (SBC) were employed in this study. The study also used the AIC for the lag length selection of the ADF model.

Step 2: Next, the parameters of the intervention function and SARIMA were estimated and determined. The autocorrelation function (ACF), partial autocorrelation function (PACF) and cross-autocorrelation function (CACF) were used to tentatively identify the parameters of the model. Nonetheless, statistical measures generally provide outstanding proof of an appropriate intervention function. The theoretical characteristics of the ACF and PACF for a stationary SARMA process were also presented.

Step 3: A residual or noise diagnostic check was done. The correlogram of Q-statistics based on the ACF and PACF of the residual was used for the residual analysis. Statistical tests such as the Jarque-Bera test for the normality of residuals and the Lagrange multiplier for the heteroscedasticity of the residuals were also used. The Breusch-Godfrey test was used to test the correlation of the residuals.

This will assist the Monetary Policy Committee of South Africa to understand the linear co-movement of the country’s exchange rate.

Empirical analysis

To execute the analysis, the study used a time series of real exchange rates for the period January 2000 to June 2017 obtained from the South African Reserve Bank database. The 2008 financial crisis is hypothesised to be a significant event influencing exchange rate movements in South Africa. The series showed upward and downward trends in conjunction with seasonal components. This implies that the real exchange rate in South Africa was not constant over the sampled period.

The Kruskal-Wallis (KW) statistic test was used to determine the presence of seasonal components. It provided significant evidence that the exchange rate holds seasonal properties as the KW test rejected the null hypothesis of no seasonal components over the alternative of seasonal components in the exchange rate series. Next, the researchers applied the SARIMA and SARIMA intervention models.

The results of applying the SARIMA model

The Augmented Dickey-Fuller test was applied to the time series. This provided sufficient evidence that the exchange rate series contained unit root with both seasonal and non-seasonal differencing of order one. Using the ADF model, a stationary time series was achieved.

While diagnosing the estimated ARIMA, all the estimated parameters are significant at 1%, 5% and 10% level of significance. The estimated Q-statistics provided significant evidence that the estimated model is a white noise process. Model parameter estimates must preferably be less than one to deem them sufficient and significant.

The results of applying the SARIMA intervention model

The intervention model used the 2008 financial crisis as intervention period. This crisis reached South Africa in March 2008. Before the estimation of an intervention model, the ADF test was applied to provide evidence that the pre-intervention time series had no unit root. The intervention model was estimated by firstly identifying the order of intervention parameters by applying various tests. Finally, the diagnostic checks for the noise proved that this was a white noise process, showing the estimated model to be valid.

The cross-autocorrelation function (CACF) showed that the 2008 financial crisis directly distressed the South African exchange rate, which caused a significant drop in import and export goods and services in the country the month after the event. The intervention effect is computed as an asymptotic change of 17%. This implies that the effect of the intervention caused a drop of 17% in the exchange rate. The same decline happened in the South African economy.

The next task was to determine which model best mimicked the data and produced fewer forecasts. This study applied four error metrics – a mean error, mean absolute error, mean percentage error and mean absolute percentage error – to measure the performance of each model. The results indicated that the model with intervention had the smallest values of all the proposed error metrics.

… the application of SARIMA intervention model can indeed explain the dynamics and impact of interruptions and changes in time series

What did the study find?

The US financial crisis was triggered in July 2007. However, the effect of the global financial crisis only reached South Africa in March 2008, with immediate and alarming consequences. Among others, it significantly impacted the exchange rate. It also led to a dramatic decline in the country’s output value since March 2008, which continued throughout 2008 and 2009 before reaching a steady state. During this period, resources were downgraded, companies were shut down causing unemployment rates to accelerate, and economic growth slowed down.

The study has found that the SARIMA model with intervention outperformed the SARIMA model, and that the application of SARIMA intervention model can indeed explain the dynamics and impact of interruptions and changes in time series.

Also, the study has shown that a seasonal time series that is interrupted by policies during a financial crisis can be modelled by the SARIMA intervention model. Going forward, scholars can also extend this empirical analysis to multivariate modelling by using the determinants of the exchange rate and the SARIMAX model with intervention to gain a better understanding of the linear relationship and co-movement of the exchange rate in South Africa.

The results of this analysis provide practical information for the Monetary Policy Committee of South Africa to make informed policy decisions on exchange rate movements. It also underlines the value of the intervention model in modelling interrupted time series such as exchange rates.

  • Original article: Makatjane, K. D., Molefe, E. K., & Van Wyk, R. B. (2018). The Analysis of the 2008 US Financial Crisis: An Intervention Approach. Journal of Economics and Behavioral Studies, 10(1), 59-68, Doi:
  • Roscoe Van Wyk is from the University of Stellenbosch Business School.

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