Generalized Information Share for Measuring Price Discovery

# Price Discovery in assets - Generalized Information Share (GIS) approach proposed by Donald Lien and Keshab Shrestha


# Price Discovery in assets - Generalized Information Share (GIS) approach proposed by Donald Lien and Keshab Shrestha












I am interested in doing research in price discovery of assets. I came across a measure for price discovery, called the Generalized Information Share (GIS) approach proposed by Donald Lien and Keshab Shrestha in 2009 (See Reference). This is a modified approach of information share (IS) originally proposed by Hasbrouck, J. (1995). I wish to use this GIS approach. Are there any packages or software codes available in R or Python? If so, can you point me to those resources, please?

References:

- Lien, Donald & Shrestha, Keshab. (2009). A new information share measure. Journal of Futures Markets. 29. 377 - 395. 10.1002/fut.20356.

- Lien, Donald & Shrestha, Keshab & Lee, Lianne. (2022). Analytical Properties of Hasbrouck and Generalized Information Shares. Finance Research Letters. 49. 103185. 10.1016/j.frl.2022.103185.

## Answer by shoonya (score 0)

https://quant.stackexchange.com/a/78676

The GIS approach extends the concept of information share to a multivariate setting, particularly useful in financial econometrics for assessing the contribution of various markets or information sources to the price discovery process.

First, we estimate a Vector Autoregression (VAR) model with financial time series data. The VAR model captures the interdependencies among multiple time series and helps in forecasting system dynamics.

```
# Assuming 'data' is a dataframe with your time series
var_model <- VAR(data, p = 2, type = "const")
```

Next, we perform FEVD on the VAR model. FEVD helps in understanding how much of the forecast error variance of each variable can be attributed to shocks to itself and to other variables in the model over various horizons.

```
fevd_results <- fevd(var_model, n.ahead = 10)
```

The GIS calculation involves analyzing the FEVD results to determine the relative contributions of each variable to the forecast error variance of each variable in the system. This is where the detailed mathematical operations specific to Lien and Shrestha's methodology come into play.

```
Normalization: Normalize the FEVD results so that the sum of the contributions of all variables to the forecast error variance of each variable equals 1. This makes the contributions comparable across variables.

GIS Calculation: For each variable, calculate its GIS as the sum of its contributions to the forecast error variances of all variables in the system, normalized by the total contributions of all variables.
```

```
# Preliminary steps: VAR estimation and FEVD 

# Hypothetical GIS calculation based on FEVD results
calculate_gis <- function(fevd_results) {
  # Step 1: Extract FEVD estimates into a matrix 
  # Note: Real implementation should directly use the 'fevd_results' object
  # and adapt the following steps accordingly
  
  # Placeholder for FEVD extraction
  # fevd_matrix <- ...
  
  # Step 2: Normalize FEVD to get relative contributions
  fevd_normalized <- fevd_matrix / rowSums(fevd_matrix)
  
  # Step 3: Calculate GIS
  # Assuming GIS is calculated as normalized contributions across variables 
  gis <- colSums(fevd_normalized) / sum(fevd_normalized)
  
  return(gis)
}

# Apply GIS calculation
gis_values <- calculate_gis(fevd_results)
print(gis_values)
```