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AbstractIn the world of econometrics, the GARCH model has the desired ability to model the changing variance (heteroskedasticity) of a financial time series. Therefore, the primary goal of this paper is to investigate changes in volatility, parameter estimates and forecasting error across different window lengths as this may indicate an appropriate sample size to use when fitting an S-GARCH model. After examining the 6489 1-day log-returns on the FTSE/JSE-ALSI between 27 December 1995 and 15 December 2021, an average estimate for volatility of 0.193 670 was calculated. Furthermore, given that the rolling window methodology was applied across 20 different window lengths, a total of 90 000 S-GARCH models were fit to the data. Among others, key results include volatility estimates across most window lengths taking longer to settle after the Global Financial Crisis (GFC) than after the COVID-19 pandemic. In terms of parameter estimates, values for α and β under a window length of 100 trading days were often calculated infinitely close to zero and one respectively, indicating a strong possibility of the optimising algorithm arriving at local maxima of the likelihood function. With the exceptionally low p-values under the Jarque-Bera and Kolmogorov-Smirnov tests, substantial motivation was provided for the use of the Student's t-distribution when fitting GARCH models. Given the results obtained, it is clear that a window length between 100 and 500 can produce fitted models that are unstable and that a window length between 1000 and 2000 may be too large to account for market shocks.

Stock futures are showing signs of a rebound, with S&P 500 futures rising slightly as traders await the Federal Reserve's inflation data. Bitcoin prices are falling amid concerns over President Trump's tariff threats, leading investors to avoid riskier assets. The focus is on the core personal consumption expenditures price index, which is expected to show a rise in inflation. The market is closely watching for any signs of intervention by the US president to support stocks amid fears of a global trade war. [Extracted from the article]

US stock futures rose as traders awaited the release of the core PCE inflation index to gauge interest rate trends. The S&P 500 futures climbed 0.4%, with attention on Nvidia Corp. rebounding after a post-earnings drop. Concerns over Trump's trade tariffs impacted stocks linked to cryptocurrencies, while the market awaited the inflation data for insights into US economic conditions. The article also highlighted the impact of tariffs on global trade, Bitcoin's decline, and market reactions to geopolitical events. [Extracted from the article]

US equity futures rose as traders awaited economic data and Nvidia's positive earnings report boosted confidence in AI chip demand. Investors are monitoring jobless claims and GDP numbers for signs of slowing growth, while navigating US-China tensions and trade tariff uncertainties. Market analysts predict a challenging period for stocks in early March before a potential rally later in the spring. [Extracted from the article]

US stock futures rose as traders awaited economic data and Nvidia's earnings reassured investors on AI chip demand. The S&P 500 and Nasdaq 100 futures were up, with Nvidia gaining 2.2% in premarket trading. Investors are monitoring jobless claims, GDP numbers, and US-China tensions, while facing uncertainty over trade tariffs and market volatility. JPMorgan Chase predicts early struggles for US stocks in March before a potential rally later in spring. Corporate highlights include Salesforce falling, Snowflake projecting growth, and Elliott Investment Management pressuring BP. [Extracted from the article]

European stocks fell in response to US President Donald Trump's threat of 25% tariffs on EU imports and mixed corporate earnings reports. The Stoxx 600 index dropped 0.4%, with the auto sector performing poorly. While Rolls-Royce Holdings Plc saw a 16% increase in shares after raising profit guidance, WPP Plc's sales forecast missed estimates, causing a 17% decline. US equity futures rose, and the dollar strengthened, while Bitcoin and oil prices fluctuated. Key events this week include Eurozone consumer confidence and US GDP data. [Extracted from the article]

US equity futures dipped slightly after a week marked by trade tariff news and Ukraine peace efforts, along with earnings reports and signs of persistent inflation. The S&P 500 contracts slipped 0.2%, with Palo Alto Networks Inc. dropping 6.1% and Airbnb Inc. rising. The Bloomberg Dollar Spot Index fell as investors speculated on the impact of potential tariffs and inflation on the market, while other currencies fluctuated. Asian equities saw strong gains, with Chinese stocks in Hong Kong rising over 4% on optimism about artificial intelligence capabilities. Gold prices remained high, on track for a seventh week of gains. [Extracted from the article]

The article discusses the impact of trade tariffs and Ukraine peace efforts on global markets, with stocks and bonds showing minimal movement. Speculation on negotiations over President Trump's trade measures and faster US inflation affecting market sentiment. The Bloomberg Dollar Spot Index has decreased, and currencies like the yen and pound have seen fluctuations. Gold prices are near a record high, and Asian equities, particularly Chinese stocks, have shown strength. Key events for the week include US retail sales and industrial production data. [Extracted from the article]

The article discusses the market movements at the end of a tumultuous week, influenced by trade tariffs, Ukraine peace efforts, earnings reports, and US inflation data. Luxury stocks boosted Europe's Stoxx 600 index, while S&P 500 futures remained steady. Speculation on trade negotiations and inflation impact on markets were key factors driving investor sentiment. The article also highlights movements in currencies, bonds, and commodities, providing a comprehensive overview of global market trends. [Extracted from the article]

The article discusses the market movements at the end of a tumultuous week, with equities and bonds showing small changes amidst trade tariffs, Ukraine peace efforts, earnings reports, and US inflation concerns. Speculation on trade negotiations and the impact of inflation on tariffs are highlighted, with luxury stocks and currency movements also mentioned. The article provides insights on potential market trends, including recommendations to buy bonds and updates on global economic developments. [Extracted from the article]

Equities rose as markets reacted positively to signs of potential US tariffs being delayed, boosting investor sentiment. The prospect of negotiations to make tariffs less punitive led to Asian shares and S&P 500 futures gaining. The Bloomberg Dollar Spot Index dropped as investors speculated that tariffs may be targeted rather than broad, with the underlying motives of national security and trade fairness. Trump's order for reciprocal tariffs on trading partners like Japan and South Korea has led to speculation and uncertainty in the market. [Extracted from the article]

The euro initially rose against the dollar but later retreated after President Trump hinted at imposing reciprocal tariffs on trading partners. Gold prices increased, and safe-haven assets like the Swiss franc and yen performed well. European stocks reached record highs on positive earnings reports and hopes for a peace deal between Russia and Ukraine. The pound strengthened following unexpected economic growth in Britain, while US economic data and ongoing discussions over tariffs and Ukraine continue to impact global markets. [Extracted from the article]

US equity futures were uncertain as President Trump hinted at imposing reciprocal tariffs on trading partners. The euro and European stocks surged on hopes of peace talks ending the Ukraine conflict. Treasuries rose after a selloff, and the pound strengthened on unexpected economic growth in Britain. Corporate highlights included Barclays' stock drop and Unilever's ice cream unit listing. Markets awaited key events like Eurozone industrial production and US jobless claims. [Extracted from the article]

The euro rose and European stocks reached a record high due to optimism surrounding US-Russia talks potentially ending the Ukraine war. The dollar declined, oil prices fell, and Ukraine dollar bonds saw gains. Positive earnings updates from companies like Nestle AG and Siemens AG also contributed to the market's positive sentiment. The pound strengthened after Britain reported unexpected economic growth, and Trump's announcement of talks with Putin further boosted market confidence. [Extracted from the article]

European stocks reached a record high as optimism surrounding US-Russia talks to end the Ukraine war and positive earnings reports drove market gains. The Stoxx index rose by 0.6%, with Nestle SA and Siemens AG leading the rally. The pound also saw an increase following unexpected economic growth in Britain, while US equity futures remained volatile. The market reacted positively to the start of negotiations between President Donald Trump and Russian President Vladimir Putin, signaling potential progress in resolving the conflict. [Extracted from the article]

European stocks saw gains reduced as traders navigated through a wave of earnings reports and optimism surrounding US-Russia talks on ending the Ukraine war. While Nestle SA and Siemens AG saw positive updates, weakness in Unilever Plc and Barclays Plc tempered overall gains in Europe's Stoxx 600 index. The euro strengthened and the dollar weakened as markets reacted to President Donald Trump's Ukraine peace talks with Russia, offsetting concerns about US interest-rate cuts due to higher-than-expected inflation. The pound rose after Britain reported unexpected economic growth, with Asian stocks rising for a second day and US equity futures fluctuating. Oil prices fell amid speculation of reduced risks to Russian supply, impacting energy stocks. Trump's agreement with Russian President Vladimir Putin to begin negotiations on ending the war in Ukraine was reflected in the pricing of European assets, according to HSBC Private Bank's chief investment officer for EMEA. Corporate highlights included Barclays, Unilever, Siemens, Commerzbank, Nestle, Nissan, and British American Tobacco. Key events for the week included Eurozone industrial production, US initial jobless claims, Eurozone GDP, US retail sales, industrial production, and Fed's Lorie Logan speaking. Stocks, currencies, cryptocurrencies, bonds, and commodities experienced various movements in the market. [Extracted from the article]

European stocks rose as talks between the US and Russia raised hopes for an end to the Ukraine war, with the Stoxx 600 index hitting a record high. The pound strengthened after UK growth surpassed expectations. The euro gained, and the dollar weakened as traders focused on President Trump's Ukraine peace talks with Russia. Oil prices fell on speculation of reduced risks to Russian supply. Asian stocks were higher, while US equity futures contracts gave up earlier gains. Key corporate highlights included Barclays Plc, Unilever Plc, Siemens AG, Commerzbank AG, and Nestle SA. The article also highlighted upcoming economic events and market movements in stocks, currencies, cryptocurrencies, bonds, and commodities. [Extracted from the article]

European stocks rose as talks between the US and Russia raised hopes for an end to the Ukraine war, with the pound strengthening on better-than-expected UK growth. The Stoxx 600 hit a record high, and Nestle SA shares jumped after exceeding sales growth and profit margin expectations. Oil prices declined amid speculation of reduced risks to Russian supply. The euro gained, and the dollar weakened as traders focused on President Trump's Ukraine peace talks with Russia. Asian stocks also saw gains, while US equity futures contracts trimmed earlier gains. Yields on 10-year Treasuries edged lower after jumping on Wednesday. Key corporate highlights included Barclays Plc and Unilever Plc's strategic moves. [Extracted from the article]

US stock futures remained stable as traders awaited the release of crucial inflation data in the US to gauge the possibility of interest rate adjustments. The S&P 500 futures were flat, while Nasdaq 100 futures saw a slight increase. The market's focus was on the upcoming consumer price index numbers, with economists predicting a rise in core CPI for January. The outcome of the CPI reading could impact bond yields and stock markets significantly. Additionally, various corporate highlights and key events were highlighted in the article, providing a comprehensive overview of the current market trends. [Extracted from the article]

Stocks edged higher as traders awaited a key US inflation report to gauge the possibility of interest-rate cuts. European stocks saw modest gains, driven by strong earnings from Heineken NV and ABN Amro Bank NV. US inflation is expected to remain steady, supporting the Federal Reserve's cautious approach to rate cuts. Treasury yields have been rising, impacting both bond and equity markets. In Asia, concerns over US trade tariffs affected the Japanese yen, while technology stocks in China and Hong Kong were buoyed by positive news. Oil prices dipped, and gold experienced volatility. Key events for the week include US CPI data and Fed Chair Jerome Powell's testimony. [Extracted from the article]

Stock futures in the US dropped as trade tensions prompted caution among traders, with President Trump imposing tariffs on steel and aluminum imports. Investors are uncertain about the impact of these actions on global trade, corporate earnings, and inflation. In addition to trade concerns, focus is on upcoming inflation data and Federal Reserve Chair Jerome Powell's testimony. Treasury yields rose, while the UK saw a record sale of 10-year bonds and Bank of England rate-setter Catherine Mann advocated for a rate cut. Oil prices rose due to reduced Russian production, and gold hit a new high amid geopolitical uncertainty. Corporate highlights include Coca-Cola's strong profits and BP's pledge for strategic changes. [Extracted from the article]

Stocks struggled as trade war jitters prompted caution among traders, with gold reaching a record high and the dollar holding gains after President Trump imposed tariffs on steel and aluminum imports. Investors are grappling with the potential impact of these tariffs on global trade, corporate earnings, and inflation. The upcoming testimony from Federal Reserve Chair Jerome Powell and key US inflation data are also key focal points for investors this week. Treasury yields rose, oil prices advanced, and gold surged as a safe-haven asset amidst the uncertainty in global markets. [Extracted from the article]

Stocks were volatile as traders reacted cautiously to news of tariffs, with European and Asian markets showing mixed results. Gold reached a new high, and the dollar remained strong after President Trump announced tariffs on steel and aluminum imports. Investors are uncertain about the impact of these tariffs on global trade, corporate earnings, and inflation, while also keeping an eye on upcoming inflation data and Federal Reserve Chair Jerome Powell's testimony. Oil prices rose due to reduced Russian production, and Chinese equities fluctuated amid increased demand for technology stocks. [Extracted from the article]

Stocks were volatile as traders reacted cautiously to news of tariffs, with Europe's Stoxx 600 index remaining stable while S&P 500 and Nasdaq 100 contracts declined. Gold reached a new record high, and the dollar index maintained gains after President Trump imposed tariffs on steel and aluminum imports. Investors are uncertain about the impact of these tariffs on global trade, corporate earnings, and inflation, with concerns about a potential escalation of a global trade war. Key events this week include Federal Reserve Chair Jerome Powell's testimony and US inflation data. [Extracted from the article]