Quarterly Average WTI Crude Oil Price (Level)

Description

Quarterly average spot price of West Texas Intermediate (WTI) crude oil at Cushing, Oklahoma.

Usage

DCOILWTICO_level

Format

A data frame with 161 observations and 2 variables:

date

Date of observation (class Date)

DCOILWTICO

Quarterly average oil price in U.S. dollars per barrel

Source

Federal Reserve Economic Data (FRED), Federal Reserve Bank of St. Louis. Data downloaded on 2026-01-27. https://fred.stlouisfed.org/

Conditional Forecast with VAR or BVAR

Description

Computes conditional forecasts using the Kalman filter and smoother methods proposed by Clarida and Coyle (1984) and Bańbura et al. (2015). Supports classical VAR models (varest from the vars package). Future implementations will also include Bayesian VAR models (bvar from the BVAR package). For now, for BVAR models the function allows analysis at the median of the parameter distribution.

Usage

cforecast(fit, cond_path, cond_var, horizon = NULL, p0 = 10000)

Arguments

Value

A list with:

• forecast — Conditional forecast matrix (horizon × variables)

• mse — Forecast mean squared error (array: K × K × horizon)

• fkf — Output of the Kalman smoother (FKF::fks)

• ss — State space representation used in the forecast

• cond_var — Indices of constrained variables

• cond_path — The conditional path used

• horizon — Effective forecast horizon

• fit — The fitted VAR/BVAR object

• y — Full data matrix (historical + future with conditional constraints)

References

Clarida, R. and D. Coyle (1984). Conditional Projection by Means of Kalman Filtering. Carnegie-Rochester Conference Series on Public Policy, 20, 247–284.

Bańbura, M., Giannone, D., & Lenza, M. (2015). Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections. International Journal of Forecasting, 31(3), 739–756.

Examples

library(vars)
data(Canada)
fit <- VAR(Canada, p = 2, type = "const")

# Define a conditional path: unemployment at 15 for 3 periods
cond_path <- matrix(rep(15, 3), ncol = 1)
cond_var <- 4  # 4th column is 'U'

conditional_forecast <- cforecast(fit = fit, cond_path = cond_path, cond_var = cond_var)
print(conditional_forecast$forecast)

Compute Conditional Forecast Composition

Description

Compute Conditional Forecast Composition

Usage

cforecast_composition(x, target_var)

Arguments

Value

a data.frame with the decomposition

Examples

library(cforecast)
library(vars)
data(fred_macro)
# Fit a  VAR model
fit <- VAR(fred_macro[,-1], p = 2, type = "const")
# compute a conditional forecast given no change in the oil price DCOILWTICO in the next period
cond_path = 0
fct_constr <- cforecast(fit, cond_path = cond_path, cond_var = 5)
# compute forecast composition for PCEPILFE
infl_composition <- cforecast_composition(fct_constr, target_var =2)

Conditional Forecast Variable Weights

Description

Computes observation weights used in the Kalman smoother for a given target variable, showing the relative contribution of observed variables to the conditional forecast.

Usage

fct_weights(fit, cond_var, target_var, horizon, p0 = 10000)

Arguments

Value

A list of weight matrices for each horizon step

Examples

library(cforecast)
library(vars)
data(fred_macro)
# Fit a  VAR model
fit <- VAR(fred_macro[,-1], p = 2, type = "const")
# compute observation weights for PCEPILFE given the conditioning on DCOILWTICO
fct_weights_fm <- fct_weights(fit = fit, cond_var = 5, target_var = 2, horizon = 1)
# note that only DCOILWTICO's weight is nonzero for h=1

U.S. Macroeconomic Dataset from FRED

Description

Source: Federal Reserve Economic Data (FRED) https://fred.stlouisfed.org/

Usage

fred_macro

Format

An object of class data.frame with 158 rows and 6 columns.

Details

Data vintage: 2026-01-27.

All variables are obtained from the Federal Reserve Economic Data (FRED) database and converted to quarterly frequency. Observations are aligned to quarter-end dates to ensure consistency across series and compatibility with quarterly VAR estimation and forecasting.

Interest-rate and spread variables are averaged within each quarter, while price indices use end-of-period quarterly values.

Variable definitions:

GDPC1

Real Gross Domestic Product. Inflation-adjusted U.S. GDP, expressed as the quarter-to-quarter percent change.

PCEPILFE

Core PCE Price Index. Personal Consumption Expenditures price index excluding food and energy (“core PCE”), expressed as the quarter-to-quarter percent change using end-of-period quarterly values.

FEDFUNDS

Federal Funds Effective Rate. The effective federal funds rate, the primary short-term monetary policy rate in the United States. Constructed as the quarterly average and expressed in annualized percentage points (levels).

BAA10YM

Corporate Credit Spread. The spread between Moody’s seasoned Baa corporate bond yield and the 10-year U.S. Treasury constant maturity yield. Averaged within each quarter and expressed in percentage points.

DCOILWTICO

Crude Oil Price (WTI). Spot price of West Texas Intermediate (WTI) crude oil at Cushing, Oklahoma. Quarterly average growth rate (quarter-to-quarter percent change).

Date convention: All quarterly observations are aligned to the last calendar day of the quarter to ensure temporal consistency across variables and compatibility with quarterly VAR and forecasting analysis.

State Space Representation

Description

Constructs the state space representation of a VAR model. Compatible with both classical VAR models (from the vars package) and Bayesian VAR models (from the BVAR package) for which the state space representation is computed at the median of the parameter distribution.

Usage

state_space_representation(fit, p0 = 10000)

Arguments

Value

A list containing the state space system matrices:

• Tt — transition matrix

• Zt — observation matrix

• GGt — observation noise covariance

• HHt — process noise covariance

• dt — deterministic component (e.g., constant)

• a0 — initial state vector

• P0 — initial state covariance (diagonal, with default value 1e4)

Author(s)

Tim Ginker

Examples

library(vars)
library(BVAR)
data(Canada)

# Classical VAR
fit_vars <- VAR(Canada, p = 2, type = "const")
ss_vars <- state_space_representation(fit_vars)

# Bayesian VAR (small example)
data <- fred_qd[, c("CPIAUCSL", "UNRATE", "FEDFUNDS")]
data <- fred_transform(data, codes = c(5, 5, 1), lag = 4)
fit_bvar <- bvar(data, lags = 2, n_draw = 1000L, n_burn = 200L, verbose = FALSE)
ss_bvar <- state_space_representation(fit_bvar)

Compute Variable Importance for Stationary VAR

Description

Computes the relative importance of each variable in a conditional forecast from a stationary VAR model. Supports both classical VAR models (from the vars package) and Bayesian VAR models (from the BVAR package) for which the computation is performed at the median of the parameter distribution.

Usage

variable_importance_stat(fit, cond_var, target_var, horizon)

Arguments

Value

A list containing two data frames:

• variable_importance — overall variable importance by horizon

• marginal_variable_importance — importance of future observations (marginal)

Examples

library(cforecast)
library(vars)
data(fred_macro)
# Fit a  VAR model
fit <- VAR(fred_macro[,-1], p = 2, type = "const")
# conditioning on the oil price, target variable is core inflation,
# horizon is set to 1 to speed up the computation
vim <- variable_importance_stat(fit = fit, cond_var = 5, target_var = 2, horizon = 1)