Data Cleaning Process for Linear Instruments

data cleaning methodology for linear instruments mathematical foundation and objectives the data cleaning process for linear financial instruments is founded on robust statistical and financial principles designed to address several key challenges in financial time series data quality enhancement transforming raw financial data into a form suitable for statistical analysis and modeling temporal consistency ensuring time series are properly aligned and sampled at regular intervals statistical robustness mitigating the impact of outliers and anomalies that could distort risk and return estimates missing data reconstruction applying principled approaches to handle missing observations cross currency normalization aligning financial data across different currency regimes duration adjustment accounting for the changing risk characteristics of fixed income instruments over time the mathematical foundation combines time series analysis, statistical inference, and financial theory to produce clean, consistent data that accurately represents the underlying financial reality time series processing methodology temporal alignment and filtering the time series processing begins with temporal alignment to ensure consistent sampling chronological ordering time series are sorted chronologically to ensure proper sequencing business day selection only business days are retained negative value removal negative prices are masked as they violate financial constraints time window selection data is truncated to a relevant time window maximum 5 years return calculation framework returns are calculated using both arithmetic and logarithmic approaches arithmetic returns r t^a = \frac{p t p {t 1}}{p {t 1}} logarithmic returns r t^l = \ln(p t / p {t 1}) = \ln(1 + r t^a) logarithmic returns are preferred for statistical analysis due to their additive property over time, while arithmetic returns maintain interpretability for financial reporting as well as portfolio aggregation statistical approaches to outlier detection and treatment outlier detection methodology outliers in financial returns are identified using a statistical approach based on standard deviation standard deviation estimation for a return series r t , the standard deviation σ is estimated using \sigma = \sqrt{\frac{\sum t(r t μ)^2}{n 1}} threshold based classification given k a configurable threshold parameter (typically 3 5), a return r t is classified as an outlier if |r t| > k·\sigma outlier treatment strategies two principal strategies are employed for handling detected outliers zero replacement outliers are considered missing values, effectively neutralizing their impact while preserving the time series structure the handling of missing values will be treated in the next section this approach is preferred when outliers are likely due to data errors rather than genuine market movements or for regressions as outliers will have a significant weight preservation outliers are retained unchanged when they are believed to represent genuine market events that should be incorporated into risk models the choice between these strategies depends on the specific financial instruments and market conditions being analyzed missing value imputation methodology a sophisticated factor based approach is used to fill missing values according to the following steps factor model specification given f i,t the risk factor returns, β i the factor exposures and ε t the idiosyncratic component, returns are modeled as r t = \alpha + \sum i(β i\cdot f {i,t}) + \epsilon t innovation generation given μ ewma and σ ewma are exponentially weighted moving averages of the residual mean and standard deviation, innovations are generated using \epsilon {t } \sim \mathcal{n}(\mu \text{ewma}, \sigma \text{ewma}) return reconstruction the missing returns are then reconstructed as r {t } = \sum i(\beta i·f {i,t}) + \epsilon {t } \quad \text{for} \quad t \in \text{missing values} this approach preserves both the systematic risk exposure and the statistical properties of the idiosyncratic component fixed income instruments duration adjustment methodology time to maturity scaling for fixed income instruments, returns are adjusted to account for the changing duration as bonds approach maturity (aka pull to par) return scaling given ttm final the time to maturity at the end of the observation period and ttm t the current time to maturity of a fixed income instruments, the returns r t are adjusted according to r t^\text{adjusted} = r t \cdot (\text{ttm} \text{final} / \text{ttm} t) this methodology ensures that bond returns are comparable across time despite their changing risk characteristics as they approach maturity, which is essential for accurate risk modeling and portfolio optimization data quality validation framework sufficiency criteria time series are validated against minimum quality standards minimum data points a time series must contain at least 20 non zero returns maximum missing ratio the proportion of missing values must not exceed a threshold of 20% error classification instruments failing the quality criteria are classified by error type insufficient data fewer than the minimum required data points expired instruments fixed income instruments past their maturity date currency mismatch missing or inconsistent currency information excessive missing values too many missing observations to reliably impute conclusion methodological significance the data cleaning methodology for linear instruments represents a principled approach to preparing financial data for analysis by combining statistical rigor with financial theory, it addresses the unique challenges of financial time series fat tailed distributions characteristic of financial returns time varying volatility that affects risk estimation cross asset dependencies that influence missing value imputation term structure effects in fixed income instruments the resulting clean data provides a solid foundation for subsequent risk modeling, portfolio optimization, and performance attribution, ensuring that financial decisions are based on accurate and consistent information