curve | R Documentation |
Fits the reserve demand curve between excess reserves and normalised rates
curve(x, y, type = "logistic", dummy = NULL, q = NULL, ...)
x |
A matrix of explanatory variables. Excess reserve must be the first input.Additional regressor follow (optional). |
y |
A vector of normalised interest rates. |
type |
The type of the reserve demand curve. This can be any of |
dummy |
Optional input to signify a regime change (vertical shifts in the curve). Must be a vector of equal length to the rows of |
q |
Target interval. This is a scalar below 1, for example 0.9 is the 90% interval. If |
... |
Additional arguments passed to optimiser |
For a description of the parametric curves, see the provided reference. Below we list their functions:
logisitc
(Logistic)
r_i = \alpha + \kappa / (1 - \beta e^{g(\bm{C}_i)}) + \varepsilon_i
redLogistic
(Reduced logistic)
r_i = \alpha + 1 / (1 - \beta e^{g(\bm{C}_i)}) + \varepsilon_i
fixLogistic
(Fixed logistic)
r_i = \alpha + 1 / (1 - e^{g(\bm{C}_i)}) + \varepsilon_i
doubleExp
(Double exponential)
r_i = \alpha + \beta e^{\rho e^{g(\bm{C}_i)}} + \varepsilon_i
exponential
(Exponential)
r_i = \alpha + \beta e^{g(\bm{C}_i)} + \varepsilon_i
fixExponential
(Fixed exponential)
r_i = \beta e^{g(\bm{C}_i)} + \varepsilon_i
arctan
(Arctangent)
r_i = \alpha + \beta \arctan ( g(\bm{C}_i)) + \varepsilon_i
linear
(Linear)
r_i = g(\bm{C}_i) + \varepsilon_i
And g(\bm{C}) = c + \bm{C} w_g
, where \alpha
, \beta
, \kappa
, \rho
are curve parameters,
c
is a constant togglable by constant
, \bm{C}
are the regressors including the excess reserves. w_g
their coefficients, and finally \varepsilon_i
is the error term of the curve.
Returns a model of class curvir
. This includes
type
the type of the curve.
constant
a logical indicating the use of a constant.
w
a list including: mean
the curve parameters for the mean of the curve, upper
and lower
the parameters for the curve at the upper and lower intervals.
data
a list including the y
, x
, and dummy
used for the fitting of the curve.
mse
the MSE from the fitting of the curve (the mean only).
q
the interval used in the fitting of the curve.
An additional column for the constant is automatically generated, unless requested otherwise.
Nikolaos Kourentzes, nikolaos@kourentzes.com
Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).
predict.curvir
, plot.curvir
, and curveopt
.
# Use ECB example data
rate <- ecb$rate
x <- ecb$x[,1,drop=FALSE]
curve(x,rate)
# An arctangent curve
curve(x,rate,type="arctan")
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