Modeling financial interval time series.

Area of Science:

• Financial econometrics
• Time series analysis
• Stochastic modeling

Background:

• Traditional financial models often rely solely on daily closing prices, potentially omitting crucial intra-day information like price ranges.
• This omission can lead to suboptimal time series modeling and forecasting in financial markets.

Purpose of the Study:

• To develop and validate an interval time series model incorporating daily maximum, minimum, and closing prices.
• To enhance financial time series forecasting by utilizing richer intra-day data.
• To accurately forecast the entire price interval.

Main Methods:

• Development of an interval time series model using maximum, minimum, and closing prices.
• Application of stochastic differential equations and the Girsanov theorem to derive the likelihood function and maximum likelihood estimators (MLEs).
• Inclusion of a stochastic volatility model to address heteroscedasticity in volatility.

Main Results:

• A simulation study demonstrated the efficiency of the proposed estimators.
• Empirical analysis using S&P 500 index data showed the proposed method's superior forecasting accuracy compared to existing alternatives.
• The interval time series model successfully forecasts the entire price range.

Conclusions:

• The proposed interval time series model effectively leverages intra-day price information (max, min, close) for improved financial forecasting.
• The method provides more accurate predictions than traditional models, particularly for volatile financial markets.
• This approach offers a valuable advancement in financial time series analysis and prediction.