Data model for the AxE-Model (Axiomatic Econometric Modeling Paradigm)

Description

Calculation of the relevant data for the AxE-model from a financial time series: trend, volatiliy, change in quotes and risk level.

Usage

axe(quotes)

Arguments

Value

data frame

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2020) Trendbasierte Prognostik. Independently Published.

Examples

set.seed(1234)
s <- 13000 + cumsum(rnorm(100))
df_axe <- axe(s)
op <- par(mfrow=c(3,1))
plot(s, type = "l")
plot(df_axe$trend5, type = "l")
abline(a = 0, b = 0)
plot(df_axe$vola5, type = "l")
par(op)

implementation of the AxE model based on the ssr-MLP

Description

Trains a 2-layer MLP with a given time series of quotes with price changes or volatility as target value. The coordinates (or independent factors) are given through the AxE model)

Usage

axe_narch_model(quotes, T, tgt)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

set.seed(1234)
n <- 250
s <- 13000 + cumsum(rnorm(n))
T = 20
# create model for 5-day trend
model <- axe_narch_model(s, T, 'trend')
# calculate prognosis for trend 
s_ <- s[n] + cumsum(rnorm(20))
s_T <- axe_narch_predict(model, s_, 'trend')
# plot the results
plot(seq(1:20), s_, type = "l", 
    xlim = c(0,21+T), ylim = c(min(s_, s_T)-5, max(s_, s_T)+5))
points(20+T, s_T, col='red', pch = 16)
# create model for 5-day vola
model <- axe_narch_model(s, T, 'vola')
r_T <- axe_narch_predict(model, s_, 'vola')
lines(c(20+T,20+T), c(s_T-r_T, s_T+r_T), col='orange')

Prediction function for the AxE-NARCH model

Description

Calculates the prediction for a given model

Usage

axe_narch_predict(model, quotes, tgt)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

set.seed(1234)
n <- 250
s <- 13000 + cumsum(rnorm(n))
T = 20
# create model for 5-day trend
model <- axe_narch_model(s, T, 'trend')
# calculate prognosis for trend 
s_ <- s[n] + cumsum(rnorm(20))
s_T <- axe_narch_predict(model, s_, 'trend')
# plot the results
plot(seq(1:20), s_, type = "l", 
    xlim = c(0,21+T), ylim = c(min(s_, s_T)-5, max(s_, s_T)+5))
points(20+T, s_T, col='red', pch = 16)
# create model for 5-day vola
model <- axe_narch_model(s, T, 'vola')
r_T <- axe_narch_predict(model, s_, 'vola')
lines(c(20+T,20+T), c(s_T-r_T, s_T+r_T), col='orange')

Factor-wise Influence Indicator (Model-fii) for a given ssrmlp model

Description

The Model-fii depicts the overall influence of the input factors on the resulting trained ssrmlp model. For computation a unit matrix is used to accumulate the weights for each factor separately.

Usage

fii_model(W)

Arguments

Value

Author(s)

Dr. Lars Metzner

Examples

# generate data
set.seed(42)
x <- rnorm(300)
y <- rnorm(300)
z <- rnorm(300) + atan2(x, y)
# coordinates
X <- matrix(cbind(x,y), ncol = 2)
Y <- as.double(z)
# Training
W <- ssrmlp_train(X, Y)
fii_model(W)

Factor-wise Influence Indicator (Prediction-fii) for a given ssrmlp model regarding a given input vector

Description

The Prediction-fii depicts the overall influence of the given input factors on the resulting prediction from a trained ssrmlp model. For computation the components of the input vectors a taken separately as input for the model.

Usage

fii_prediction(W, x)

Arguments

Value

Author(s)

Dr. Lars Metzner

Examples

# generate data
set.seed(42)
x <- rnorm(300)
y <- rnorm(300)
z <- rnorm(300) + atan2(x, y)
# coordinates
X <- matrix(cbind(x,y), ncol = 2)
Y <- as.double(z)
# Training
W <- ssrmlp_train(X, Y)
fii_prediction(W, X)

Loading a ssrmlp model from ONNX file

Description

Loading a ssrmlp model from ONNX file (also see onnx.ai). This function uses the onnx python implementation, hence a python environment including modules onnx and numpy is required.

Usage

onnx_load(filename)

Arguments

Value

Author(s)

Dr. Lars Metzner

Examples

# generate data
set.seed(42)
x <- rnorm(300)
y <- rnorm(300)
z <- rnorm(300) + atan2(x, y)
# coordinates
X <- matrix(cbind(x,y), ncol = 2)
Y <- as.double(z)
# Training
ssrmlp_model <- ssrmlp_train(X, Y)
# only if python is available
if (reticulate::py_module_available('onnx')) {
  tryCatch( 
    {
      # save in ONNX format
      onnx_save(ssrmlp_model, 'file.onnx')
      # loading the file in ONNX format
      W <- onnx_load('file.onnx')
      # prediction with original implementation
      p <- t(c(0.25, 0.25))
      pred <- ssrmlp_predict(p, W) 
      # and now test with onnxruntime.ai
    },
    error = function(cond) {
      message(conditionMessage(cond))
    },
    finally = {
      # cleanup
      file.remove('file.onnx')
      # to avoid NOTE in R CHECK
      tempfile <-  reticulate::import("tempfile")
      tmp <- tempfile$gettempdir()
      if (dir.exists(file.path(tmp, "__pycache__"))) {
        unlink(file.path(tmp, "__pycache__"), recursive = TRUE, force = TRUE)
      }
      tmp_py_files <- list.files(tmp, 
                                 pattern = "^__autograph_generated_file.*py$", full.names = TRUE)
      file.remove(tmp_py_files)
      print("done")
    }
  )
}

Saving a ssrmlp model in onnx format to file

Description

Saving a ssrmlp model in onnx format to file (also see onnx.ai). This function uses the onnx python implementation, hence a python environment including modules onnx and numpy is required.

Usage

onnx_save(ssrmlp_model, filename)

Arguments

Author(s)

Dr. Lars Metzner

Examples

# generate data
set.seed(42)
x <- rnorm(300)
y <- rnorm(300)
z <- rnorm(300) + atan2(x, y)
# coordinates
X <- matrix(cbind(x,y), ncol = 2)
Y <- as.double(z)
# Training
ssrmlp_model <- ssrmlp_train(X, Y)
# prediction
p <- t(c(0.25, 0.25))
pred <- ssrmlp_predict(p, ssrmlp_model) 
# only if python is available
if (reticulate::py_module_available('onnx')) {
  tryCatch( 
    {
      # save in ONNX format
      onnx_save(ssrmlp_model, 'file.onnx')
      # and now test with onnxruntime.ai
    },
    error = function(cond) {
      message(conditionMessage(cond))
    },
    finally = {
      # cleanup
      file.remove('file.onnx')
      # to avoid NOTE in R CHECK
      tempfile <-  reticulate::import("tempfile")
      tmp <- tempfile$gettempdir()
      if (dir.exists(file.path(tmp, "__pycache__"))) {
        unlink(file.path(tmp, "__pycache__"), recursive = TRUE, force = TRUE)
      }
      tmp_py_files <- list.files(tmp, 
                                 pattern = "^__autograph_generated_file.*py$", full.names = TRUE)
      file.remove(tmp_py_files)
      print("done")
    }
  )
}

Partial Sum Plot

Description

Plots the Partial Sums with their quantiles for a given set of observations und the corresponding regression function.

Usage

psplot(dat, mu, text = 'Sample')

Arguments

Value

No explicit return value: a plot is generated

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

psplot(sin(seq(-pi, pi, length.out = 200))+rnorm(200),
  sin(seq(-pi, pi, length.out = 200)), text='Test')

Partial Sum Plot for 2-dimensional coordinates

Description

Plots the partial sum statistic for the 3-dimensional SSR model

Usage

psplot3d(koord, z, mu, text = "Sample")

Arguments

Value

No explicit return value: a plot is generated

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(1234)
x <- rnorm(900)
y <- rnorm(900)
xy <- data.frame(x=x, y=y)
z <- rnorm(900) + atan2(x, y)
# Training
df_model <- ssr3d(xy, z, k = 4, fn = 8)
# plot partial sum statistic
psplot3d(xy, z, df_model$mu, 'ssr3d')

Partial Sum Plot for the multidimensional coordinates

Description

plots the partial sum statistic for the general n-dimensional SSR-model

Usage

psplotnd(koord, dat, mu, text = "Sample")

Arguments

Value

No explicit return value: a plot is generated

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(1234)
x <- rnorm(900)
y <- rnorm(900)
xy <- data.frame(x=x, y=y)
z <-data.frame(z=rnorm(900) + atan2(x, y))
# Training
df_model <- ssrnd(xy, z, k = 4, fn = 8)
# plot partial sum statistic
psplotnd(xy, z, df_model$mu, 'ssr3d')

Partial Sum Plot for the multidimensional coordinates - reworked

Description

plots the partial sum statistic for the general n-dimensional SSR-model

Usage

psplotnd2(koord, dat, mu, text = "Sample", maxint = NULL, resultplot = TRUE, accept = 10)

Arguments

Value

TRUE if Partial Sum criterion is passed or result is accepted, FALSE otherwise

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(42)
x_ <- y_ <- seq(-3, 3, length=20)
xy <- expand.grid(x=x_,y=y_)
x <- xy$x
y <- xy$y
z <- rnorm(400) + atan2(x, y)
# coordinates
X <- matrix(cbind(x, y), ncol = 2)
Y <- as.double(z)
# Training
W <- ssrmlp2_train(X, Y, accept=0) # passed: ps=39.04, secs 24.8, 250 Iterationen
Yp <- ssrmlp_predict(X, W)
psplotnd2(W$X, W$Y, W$Yp, 'ssrMLP2', resultplot = TRUE)

Partial Sum Validity Check

Description

Checks, if a given regression function is adequate with respect to the partial sum criterium.

Usage

psvalid(dat,mu)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

psvalid(sin(seq(-pi, pi, length.out = 200))+rnorm(200), 
        sin(seq(-pi, pi, length.out = 200)))

Maximum Run Validity Check

Description

Checks, if a given regression function is adequate with respect to the maximum run criterium.

Usage

runvalid(dat,mu,k=NULL)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

runvalid(sin(seq(-pi, pi, length.out = 200))+rnorm(200)/2, 
          sin(seq(-pi, pi, length.out = 200)))

S-NARCH Model

Description

Calculates the long-, middle- and short-term trends and vola for a financial time series.

Usage

snarch(dat)

Arguments

Value

data frame

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2019) Finanzmathematische Zeitreihenanalyse. Independently Published.

Examples

# generate test data
set.seed(1234)
x <- seq(1:250)
dat <- 13000 + cumsum(rnorm(250))
# calculate the S-NARCH model
df <- snarch(dat)
# plot the results
op <- par(mfrow=c(1,3))
plot(x,dat)
lines(x,df$tr20)
lines(x,df$tr20 - df$vl20, lty = 'dotted')
lines(x,df$tr20 + df$vl20, lty = 'dotted')
plot(x,dat)
lines(x,df$tr10)
lines(x,df$tr10 - df$vl10, lty = 'dotted')
lines(x,df$tr10 + df$vl10, lty = 'dotted')
plot(x,dat)
lines(x,df$tr5)
lines(x,df$tr5 - df$vl5, lty = 'dotted')
lines(x,df$tr5 + df$vl5, lty = 'dotted')
par(op)

Onedimensional SSR-model calculation

Description

Calculates L1- and L2-functions satisfiying the partial sum criterium.

Usage

ssr(df, y1=NULL, yn=NULL, fn=0, iter=10000, 
        minStat=FALSE, ne=TRUE, l1=TRUE, ps=TRUE)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate equidistant data
set.seed(1234)
x <- seq(0, 2*pi, length.out = 200)
y <- 4*sin(x) + rnorm(200)
df <- data.frame(x=x, y=y)
# calculate regression functions
l1 <- ssr(df, ne=FALSE, ps=FALSE)
l2 <- ssr(df, ne=FALSE, l1=FALSE)
lmin <- ssr(df, ne=FALSE, minStat=TRUE, ps=FALSE)
# plot results
plot(x, y, main = 'Sign-Simplicity-Regression', 
        xlab = 't', ylab = 'sin(t)+noise')
lines(x, l1, col = 'blue')
lines(x, l2, col = 'red')
lines(x, lmin, col = 'purple')
legend("topleft", inset=c(0.01,0.01), 
        legend=c("L1 run-crit.", "L2 ps-crit.", "L1 min-stat."),
        col=c("blue", "red", "purple"), lty=1:1)

# generate nonequidistant data
df <- data.frame(x=runif(500, min=-1, max=1)*pi)
df$y <- sin(df$x)*20 + rnorm(nrow(df), mean=0, sd=10)
# calculate regression function
dfl1 <- ssr(df, fn = 5)
# plot results
plot(df)
lines(dfl1, col = 'red')

3-dimensional SSR model

Description

Calculates the regression function for the 3-dimensional SSR-model.

Usage

ssr3d(koord, dat, k = NULL, fn = NULL, iter = 1000)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(1234)
x <- rnorm(900)
y <- rnorm(900)
xy <- data.frame(x=x, y=y)
z <- rnorm(900) + atan2(x, y)
# Training
df_model <- ssr3d(xy, z)

3-dimensional SSR model prediction

Description

Calculates the prediction for a given 3-dimensional SSR model.

Usage

ssr3d_predict(df_model, xy, ms = FALSE)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(1234)
x <- rnorm(900)
y <- rnorm(900)
xy <- data.frame(x=x, y=y)
z <- rnorm(900) + atan2(x, y)
# Training
df_model <- ssr3d(xy, z)
# Prediction
xx <- c(c(0,1), c(-1,1), c(1,-1))
xx <- matrix(xx, ncol = 2)
yy <- ssr3d_predict(df_model, xx)

SSR model Prediction

Description

Calculates the prediction for a given SSR model.

Usage

ssr_predict(df, xx)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

  set.seed(1234)
  df <- data.frame(x=runif(500, min=-1, max=1)*pi)
  df$y <- sin(df$x)*20 + rnorm(nrow(df), mean=0, sd=10)
  plot(df, xlim=c(-4, 4))
  dfl1 <- ssr(df)
  lines(dfl1)
  xx <- c(-4, -1, 0, 1, 4)
  yy <- ssr_predict(dfl1, xx)
  points(xx,yy, pch='+', col='red', cex=2)

2-layer MLP with partial sum optimization - reworked

Description

Calculates the weights of a 2-layer MLP with respect to the partial sums critereon

Usage

ssrmlp2_train(X, Y, std=TRUE, opt='ps', hl=NULL, W=NULL, 
  k=NULL, fn=NULL, eta=0.5, accept = 10, maxIter=1000, alpha=NULL, beta=NULL)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(42)
x <- rnorm(300)
y <- rnorm(300)
z <- rnorm(300) + atan2(x, y)
# coordinates
X <- matrix(cbind(x,y), ncol = 2)
Y <- as.double(z)
# Training
W <- ssrmlp2_train(X, Y)

Prediction function for the ssrMLP

Description

Calculates the prediction for a given ssrMLP

Usage

ssrmlp_predict(X, W)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(42)
x <- rnorm(300)
y <- rnorm(300)
z <- rnorm(300) + atan2(x, y)
# coordinates
X <- matrix(cbind(x,y), ncol = 2)
Y <- as.double(z)
# Training
W <- ssrmlp_train(X, Y)
Yp <- ssrmlp_predict(X, W)

2-layer MLP with partial sum optimization

Description

Calculates the weights of a 2-layer MLP with respect to the partial sums critereon

Usage

ssrmlp_train(X, Y, std=TRUE, opt='ps', hl = NULL, W = NULL,
  k=10, fn=4, eta=0.75, maxIter=1000,
  facfct_ex = NULL, errfct_ex = NULL, alpha = NULL)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(42)
x <- rnorm(300)
y <- rnorm(300)
z <- rnorm(300) + atan2(x, y)
# coordinates
X <- matrix(cbind(x,y), ncol = 2)
Y <- as.double(z)
# Training
W <- ssrmlp_train(X, Y)

Multi-dimensional SSR model

Description

Calculates the multi-dimensional SSR model

Usage

ssrnd(koord, dat, k = NULL, fn = NULL, iter = 1000)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(1234)
x <- rnorm(300)
y <- rnorm(300)
xy <- data.frame(x=x, y=y)
z <-data.frame(z=rnorm(300) + atan2(x, y))
# Training
df_model <- ssrnd(xy, z)

Multi-dimensional SSR model - reworked

Description

Calculates the multi-dimensional SSR model

Usage

ssrnd2(X, Y, mdl=NULL, k=NULL, fn=NULL, n_l1=NULL, iter=1000, eps=0.0001)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(1234)
x <- rnorm(400)
y <- rnorm(400)
z <- rnorm(400) + atan2(x, y)
X <- matrix(cbind(x, y), ncol = 2)
Y <- as.double(z)

# Training
mdl <- ssrnd2(X, Y)

Near Neighborhood Estimator for Multi-dimensional SSR model

Description

Calculates the Near Neighborhood Estimator in a multi-dimensional SSR model

Usage

ssrnd2NN(X, Y, k, weighted=FALSE)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(1234)
x <- rnorm(400)
y <- rnorm(400)
z <- rnorm(400) + atan2(x, y)
X <- matrix(cbind(x, y), ncol = 2)
Y <- as.double(z)

# Training
mdl <- ssrnd2NN(X, Y, 10)

Prediction function for the multi-dimensional SSR model - reworked

Description

Calculates the prediction for a given multi-dimensional SSR model

Usage

ssrnd2_predict(mdl, xx)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(1234)
x <- rnorm(400)
y <- rnorm(400)
z <- rnorm(400) + atan2(x, y)
X <- matrix(cbind(x, y), ncol = 2)
Y <- as.double(z)

# Training
mdl <- ssrnd2(X, Y)
yy <- ssrnd2_predict(mdl, X)

Prediction function for the multi-dimensional SSR model

Description

Calculates the prediction for a given multi-dimensional SSR model

Usage

ssrnd_predict(df_model, xx)

Arguments

Value

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2021) Adäquates Maschinelles Lernen. Independently Published.

Examples

# generate data
set.seed(1234)
x <- rnorm(300)
y <- rnorm(300)
xy <- data.frame(x=x, y=y)
z <-data.frame(z=rnorm(300) + atan2(x, y))
# Training
df_model <- ssrnd(xy, z)
# Prediction
xx <- c(c(0,1), c(-1,1), c(1,-1))
xx <- matrix(xx, ncol = 2)
yy <- ssrnd_predict(df_model, xx)

Trend-based Correlation

Description

Calculates the trend-based correlation of two time series based on the trend function (Metzner's Tau)

Usage

tauM(x, y)

Arguments

Value

trend-based correlation.

Author(s)

Dr. Lars Metzner

References

Dr. Lars Metzner (2020) Trendbasierte Prognostik. Independently Published.

Examples

set.seed(1234)
s <- seq(-pi, pi, length.out = 200)
x <- s + rnorm(200)
y <- exp(s) + 5*rnorm(length(s))
op <- par(mfrow=c(1,2))
plot(x)
plot(y)
par(op)

p <- cor(x,y) # 0.5037
t <- cor(x,y, method = 'kendall') # 0.2959
tm <- tauM(x, y) # 0.0867