{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Multiple Comparisons" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "_This setup code is required to run in an IPython notebook_" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn\n", "\n", "seaborn.set_style(\"darkgrid\")\n", "plt.rc(\"figure\", figsize=(16, 6))\n", "plt.rc(\"savefig\", dpi=90)\n", "plt.rc(\"font\", family=\"sans-serif\")\n", "plt.rc(\"font\", size=14)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Reproducability\n", "import numpy as np\n", "\n", "gen = np.random.default_rng(23456)\n", "# Common seed used throughout\n", "seed = gen.integers(0, 2**31 - 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The multiple comparison procedures all allow for examining aspects of superior predictive ability. There are three available:\n", "\n", "* `SPA` - The test of Superior Predictive Ability, also known as the Reality Check (and accessible as `RealityCheck`) or the bootstrap data snooper, examines whether any model in a set of models can outperform a benchmark.\n", "* `StepM` - The stepwise multiple testing procedure uses sequential testing to determine which models are superior to a benchmark.\n", "* `MCS` - The model confidence set which computes the set of models which with performance indistinguishable from others in the set.\n", "\n", "All procedures take **losses** as inputs. That is, smaller values are preferred to larger values. This is common when evaluating forecasting models where the loss function is usually defined as a positive function of the forecast error that is increasing in the absolute error. Leading examples are Mean Square Error (MSE) and Mean Absolute Deviation (MAD)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The test of Superior Predictive Ability (SPA)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This procedure requires a $t$-element array of benchmark losses and a $t$ by $k$-element array of model losses. The null hypothesis is that no model is better than the benchmark, or \n", "\n", "$$ H_0: \\max_i E[L_i] \\geq E[L_{bm}] $$\n", "\n", "where $L_i$ is the loss from model $i$ and $L_{bm}$ is the loss from the benchmark model.\n", "\n", "This procedure is normally used when there are many competing forecasting models such as in the study of technical trading rules. The example below will make use of a set of models which are all equivalently good to a benchmark model and will serve as a *size study*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Study Design" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The study will make use of a measurement error in predictors to produce a large set of correlated variables that all have equal expected MSE. The benchmark will have identical measurement error and so all models have the same expected loss, although will have different forecasts.\n", "\n", "The first block computed the series to be forecast." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import statsmodels.api as sm\n", "from numpy.random import randn\n", "\n", "t = 1000\n", "factors = randn(t, 3)\n", "beta = np.array([1, 0.5, 0.1])\n", "e = randn(t)\n", "y = factors.dot(beta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next block computes the benchmark factors and the model factors by contaminating the original factors with noise. The models are estimated on the first 500 observations and predictions are made for the second 500. Finally, losses are constructed from these predictions." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Measurement noise\n", "bm_factors = factors + randn(t, 3)\n", "# Fit using first half, predict second half\n", "bm_beta = sm.OLS(y[:500], bm_factors[:500]).fit().params\n", "# MSE loss\n", "bm_losses = (y[500:] - bm_factors[500:].dot(bm_beta)) ** 2.0\n", "# Number of models\n", "k = 500\n", "model_factors = np.zeros((k, t, 3))\n", "model_losses = np.zeros((500, k))\n", "for i in range(k):\n", " # Add measurement noise\n", " model_factors[i] = factors + randn(1000, 3)\n", " # Compute regression parameters\n", " model_beta = sm.OLS(y[:500], model_factors[i, :500]).fit().params\n", " # Prediction and losses\n", " model_losses[:, i] = (y[500:] - model_factors[i, 500:].dot(model_beta)) ** 2.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally the SPA can be used. The SPA requires the **losses** from the benchmark and the models as inputs. Other inputs allow the bootstrap sued to be changed or for various options regarding studentization of the losses. `compute` does the real work, and then `pvalues` contains the probability that the null is true given the realizations.\n", "\n", "In this case, one would not reject. The three p-values correspond to different re-centerings of the losses. In general, the `consistent` p-value should be used. It should always be the case that\n", "\n", "$$ lower \\leq consistent \\leq upper .$$\n", "\n", "See the original papers for more details." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "lower 0.005\n", "consistent 0.005\n", "upper 0.005\n", "dtype: float64" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from arch.bootstrap import SPA\n", "\n", "spa = SPA(bm_losses, model_losses, seed=seed)\n", "spa.compute()\n", "spa.pvalues" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same blocks can be repeated to perform a simulation study. Here I only use 100 replications since this should complete in a reasonable amount of time. Also I set `reps=250` to limit the number of bootstrap replications in each application of the SPA (the default is a more reasonable 1000)." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "10\n", "20\n", "30\n", "40\n", "50\n", "60\n", "70\n", "80\n", "90\n" ] } ], "source": [ "# Save the pvalues\n", "pvalues = []\n", "b = 100\n", "seeds = gen.integers(0, 2**31 - 1, b)\n", "# Repeat 100 times\n", "for j in range(b):\n", " if j % 10 == 0:\n", " print(j)\n", " factors = randn(t, 3)\n", " beta = np.array([1, 0.5, 0.1])\n", " e = randn(t)\n", " y = factors.dot(beta)\n", "\n", " # Measurement noise\n", " bm_factors = factors + randn(t, 3)\n", " # Fit using first half, predict second half\n", " bm_beta = sm.OLS(y[:500], bm_factors[:500]).fit().params\n", " # MSE loss\n", " bm_losses = (y[500:] - bm_factors[500:].dot(bm_beta)) ** 2.0\n", " # Number of models\n", " k = 500\n", " model_factors = np.zeros((k, t, 3))\n", " model_losses = np.zeros((500, k))\n", " for i in range(k):\n", " model_factors[i] = factors + randn(1000, 3)\n", " model_beta = sm.OLS(y[:500], model_factors[i, :500]).fit().params\n", " # MSE loss\n", " model_losses[:, i] = (y[500:] - model_factors[i, 500:].dot(model_beta)) ** 2.0\n", " # Lower the bootstrap replications to 250\n", " spa = SPA(bm_losses, model_losses, reps=250, seed=seeds[j])\n", " spa.compute()\n", " pvalues.append(spa.pvalues)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally the pvalues can be plotted. Ideally they should form a $45^o$ line indicating the size is correct. Both the consistent and upper perform well. The lower has too many small p-values." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pandas as pd\n", "\n", "pvalues = pd.DataFrame(pvalues)\n", "for col in pvalues:\n", " values = pvalues[col].values\n", " values.sort()\n", " pvalues[col] = values\n", "# Change the index so that the x-values are between 0 and 1\n", "pvalues.index = np.linspace(0.005, 0.995, 100)\n", "fig = pvalues.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Power" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The SPA also has power to reject then the null is violated. The simulation will be modified so that the amount of measurement error differs across models, and so that some models are actually better than the benchmark. The p-values should be small indicating rejection of the null." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "lower 0.039\n", "consistent 0.049\n", "upper 0.050\n", "dtype: float64" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Number of models\n", "k = 500\n", "model_factors = np.zeros((k, t, 3))\n", "model_losses = np.zeros((500, k))\n", "for i in range(k):\n", " scale = (2500.0 - i) / 2500.0\n", " model_factors[i] = factors + scale * randn(1000, 3)\n", " model_beta = sm.OLS(y[:500], model_factors[i, :500]).fit().params\n", " # MSE loss\n", " model_losses[:, i] = (y[500:] - model_factors[i, 500:].dot(model_beta)) ** 2.0\n", "\n", "spa = SPA(bm_losses, model_losses, seed=seed)\n", "spa.compute()\n", "spa.pvalues" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the average losses are plotted. The higher index models are clearly better than the lower index models -- and the benchmark model (which is identical to model.0)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model_losses = pd.DataFrame(model_losses, columns=[\"model.\" + str(i) for i in range(k)])\n", "avg_model_losses = pd.DataFrame(model_losses.mean(0), columns=[\"Average loss\"])\n", "fig = avg_model_losses.plot(style=[\"o\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stepwise Multiple Testing (StepM)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Stepwise Multiple Testing is similar to the SPA and has the same null. The primary difference is that it identifies the set of models which are better than the benchmark, rather than just asking the basic question if any model is better. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model indices:\n", "['379', '466', '475']\n" ] } ], "source": [ "from arch.bootstrap import StepM\n", "\n", "stepm = StepM(bm_losses, model_losses)\n", "stepm.compute()\n", "print(\"Model indices:\")\n", "print([model.split(\".\")[1] for model in stepm.superior_models])" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "better_models = pd.concat([model_losses.mean(0), model_losses.mean(0)], 1)\n", "better_models.columns = [\"Same or worse\", \"Better\"]\n", "better = better_models.index.isin(stepm.superior_models)\n", "worse = np.logical_not(better)\n", "better_models.loc[better, \"Same or worse\"] = np.nan\n", "better_models.loc[worse, \"Better\"] = np.nan\n", "fig = better_models.plot(style=[\"o\", \"s\"], rot=270)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Model Confidence Set" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model confidence set takes a set of **losses** as its input and finds the set which are not statistically different from each other while controlling the familywise error rate. The primary output is a set of p-values, where models with a pvalue above the size are in the MCS. Small p-values indicate that the model is easily rejected from the set that includes the best. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MCS P-values\n", " Pvalue\n", "Model name \n", "model.20 0.001\n", "model.0 0.003\n", "model.120 0.005\n", "model.100 0.005\n", "model.140 0.011\n", "model.60 0.074\n", "model.40 0.101\n", "model.160 0.118\n", "model.380 0.216\n", "model.300 0.287\n", "model.80 0.443\n", "model.180 0.443\n", "model.220 0.443\n", "model.460 0.506\n", "model.340 0.536\n", "model.200 0.619\n", "model.240 0.740\n", "model.360 0.840\n", "model.400 0.840\n", "model.320 0.840\n", "model.260 0.840\n", "model.420 0.840\n", "model.280 0.840\n", "model.440 0.840\n", "model.480 1.000\n", "Included\n", "['160', '180', '200', '220', '240', '260', '280', '300', '320', '340', '360', '380', '40', '400', '420', '440', '460', '480', '80']\n", "Excluded\n", "['0', '100', '120', '140', '20', '60']\n" ] } ], "source": [ "from arch.bootstrap import MCS\n", "\n", "# Limit the size of the set\n", "losses = model_losses.iloc[:, ::20]\n", "mcs = MCS(losses, size=0.10)\n", "mcs.compute()\n", "print(\"MCS P-values\")\n", "print(mcs.pvalues)\n", "print(\"Included\")\n", "included = mcs.included\n", "print([model.split(\".\")[1] for model in included])\n", "print(\"Excluded\")\n", "excluded = mcs.excluded\n", "print([model.split(\".\")[1] for model in excluded])" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "status = pd.DataFrame(\n", " [losses.mean(0), losses.mean(0)], index=[\"Excluded\", \"Included\"]\n", ").T\n", "status.loc[status.index.isin(included), \"Excluded\"] = np.nan\n", "status.loc[status.index.isin(excluded), \"Included\"] = np.nan\n", "fig = status.plot(style=[\"o\", \"s\"])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 4 }