plot_gen.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import fft\n",
    "from scipy import stats\n",
    "import scipy\n",
    "import math\n",
    "from matplotlib.gridspec import GridSpec\n",
    "import statsmodels.tsa.stattools\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "plt.rcParams['pgf.texsystem'] = 'pdflatex'\n",
    "plt.rcParams.update({'font.family': 'serif',\n",
    "                     'text.usetex': True,\n",
    "                     'font.serif': ['Helvetica'],\n",
    "                     'font.size': 8,\n",
    "                     'axes.labelsize': 10,\n",
    "                     'axes.titlesize': 12,\n",
    "                     'figure.titlesize': 14})\n",
    "props = dict(edgecolor=\"none\", facecolor='white', alpha=0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [],
   "source": [
    "length = 10000\n",
    "lengthfGn = length\n",
    "OneOverDelta_t = 10\n",
    "Delta_t = 1/OneOverDelta_t\n",
    "band_size = 10\n",
    "band_sizefGn = band_size\n",
    "freqs = 2*math.pi*fft.fftfreq(2*length*OneOverDelta_t*band_size,Delta_t)[:length*OneOverDelta_t*band_size:band_size]\n",
    "freqsfGn = 2*math.pi*fft.fftfreq(2*lengthfGn*OneOverDelta_t*band_sizefGn,Delta_t)[:lengthfGn*OneOverDelta_t*band_sizefGn:band_sizefGn]\n",
    "theta = 1\n",
    "sigma = 1\n",
    "\n",
    "nlags = 20\n",
    "tau = 0.5 # tau defines the time lag in units of full time steps for the calculation of autocorrelation\n",
    "lags = np.arange(0, nlags*tau, tau)\n",
    "lags_th = np.arange(0,nlags*tau,0.01)\n",
    "\n",
    "H=0.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Created on Fri Aug 14 00:06:57 2020\n",
    "\n",
    "@author: Justin Yu\n",
    "\n",
    "Implementation of Fractional Brownian Motion, Hosking's method.\n",
    "\"\"\"\n",
    "def hosking(T, N, H):\n",
    "    '''\n",
    "    Generates sample paths of fractional Brownian Motion using the Davies Harte method\n",
    "    \n",
    "    args:\n",
    "        T:      length of time (in years)\n",
    "        N:      number of time steps within timeframe\n",
    "        H:      Hurst parameter\n",
    "    '''\n",
    "    gamma = lambda k,H: 0.5*(np.abs(k-1)**(2*H) - 2*np.abs(k)**(2*H) + np.abs(k+1)**(2*H))  \n",
    "    \n",
    "    X = [np.random.standard_normal()]\n",
    "    mu = [gamma(1,H)*X[0]]\n",
    "    sigsq = [1 - (gamma(1,H)**2)]\n",
    "    tau = [gamma(1,H)**2]\n",
    "    \n",
    "    d = np.array([gamma(1,H)])\n",
    "    \n",
    "    for n in range(1, N):\n",
    "        \n",
    "        F = np.rot90(np.identity(n+1))\n",
    "        c = np.array([gamma(k+1,H) for k in range(0,n+1)])\n",
    "                \n",
    "        # sigma(n+1)**2\n",
    "        s = sigsq[n-1] - ((gamma(n+1,H) - tau[n-1])**2)/sigsq[n-1]\n",
    "        \n",
    "        # d(n+1)\n",
    "        phi = (gamma(n+1,H) - tau[n-1])/sigsq[n-1]\n",
    "        d = d - phi*d[::-1]\n",
    "        d = np.append(d, phi)        \n",
    "        \n",
    "        # mu(n+1) and tau(n+1)\n",
    "        Xn1 = mu[n-1] + sigsq[n-1]*np.random.standard_normal()\n",
    "        \n",
    "        X.append(Xn1)\n",
    "        sigsq.append(s)\n",
    "        mu.append(d @ X[::-1])\n",
    "        tau.append(c @ F @ d)\n",
    "    \n",
    "    fBm = np.cumsum(X)*(N**(-H))    \n",
    "    return (T**H)*fBm\n",
    "\n",
    "\n",
    "# -*- coding: utf-8 -*-\n",
    "\"\"\"\n",
    "Created on Fri Jul  3 15:26:14 2020\n",
    "\n",
    "@author: Justin Yu, M.S. Financial Engineering, Stevens Institute of Technology\n",
    "\n",
    "Implementation of Fractional Brownian Motion, Davies Harte Method\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "def davies_harte(T, N, H):\n",
    "    '''\n",
    "    Generates sample paths of fractional Brownian Motion using the Davies Harte method\n",
    "    \n",
    "    args:\n",
    "        T:      length of time (in years)\n",
    "        N:      number of time steps within timeframe\n",
    "        H:      Hurst parameter\n",
    "    '''\n",
    "    gamma = lambda k,H: 0.5*(np.abs(k-1)**(2*H) - 2*np.abs(k)**(2*H) + np.abs(k+1)**(2*H))  \n",
    "    g = [gamma(k,H) for k in range(0,N)];    r = g + [0] + g[::-1][0:N-1]\n",
    "\n",
    "    # Step 1 (eigenvalues)\n",
    "    j = np.arange(0,2*N);   k = 2*N-1\n",
    "    lk = np.fft.fft(r*np.exp(2*np.pi*complex(0,1)*k*j*(1/(2*N))))[::-1]\n",
    "\n",
    "    # Step 2 (get random variables)\n",
    "    Vj = np.zeros((2*N,2), dtype=np.complex64); \n",
    "    Vj[0,0] = np.random.standard_normal();  Vj[N,0] = np.random.standard_normal()\n",
    "    \n",
    "    for i in range(1,N):\n",
    "        Vj1 = np.random.standard_normal();    Vj2 = np.random.standard_normal()\n",
    "        Vj[i][0] = Vj1; Vj[i][1] = Vj2; Vj[2*N-i][0] = Vj1;    Vj[2*N-i][1] = Vj2\n",
    "    \n",
    "    # Step 3 (compute Z)\n",
    "    wk = np.zeros(2*N, dtype=np.complex64)   \n",
    "    wk[0] = np.sqrt((lk[0]/(2*N)))*Vj[0][0];          \n",
    "    wk[1:N] = np.sqrt(lk[1:N]/(4*N))*((Vj[1:N].T[0]) + (complex(0,1)*Vj[1:N].T[1]))       \n",
    "    wk[N] = np.sqrt((lk[0]/(2*N)))*Vj[N][0]       \n",
    "    wk[N+1:2*N] = np.sqrt(lk[N+1:2*N]/(4*N))*(np.flip(Vj[1:N].T[0]) - (complex(0,1)*np.flip(Vj[1:N].T[1])))\n",
    "    \n",
    "    Z = np.fft.fft(wk);     fGn = Z[0:N] \n",
    "    fBm = np.cumsum(fGn)*(N**(-H))\n",
    "    fBm = (T**H)*(fBm)\n",
    "    path = np.array([0] + list(fBm))\n",
    "    return path\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/tz/fzy4bpxd7j54282vbs0hj3cm0000gn/T/ipykernel_90868/3241871123.py:5: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  fGn_th_spec = (H*np.pi)**-1*math.gamma(1-2*H)*np.cos(H*np.pi)*np.sin(H*np.pi)*math.gamma(2*H+1)*np.array([(x*2*np.pi)**(1-2*H) for x in freqsfGn])\n",
      "/var/folders/tz/fzy4bpxd7j54282vbs0hj3cm0000gn/T/ipykernel_90868/3241871123.py:6: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  uH_th_spec = (H*np.pi)**-1*math.gamma(1-2*H)*np.cos(H*np.pi)*np.sin(H*np.pi)*math.gamma(2*H+1)*np.array([sigma**2*(x*2*np.pi)**(1-2*H)/(theta**2+x**2) for x in freqs])\n",
      "/var/folders/tz/fzy4bpxd7j54282vbs0hj3cm0000gn/T/ipykernel_90868/3241871123.py:7: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  duH_th_spec = (H*np.pi)**-1*math.gamma(1-2*H)*np.cos(H*np.pi)*np.sin(H*np.pi)*math.gamma(2*H+1)*np.array([sigma**2*x**2*(x*2*np.pi)**(1-2*H)/(theta**2+x**2) for x in freqs])\n",
      "/var/folders/tz/fzy4bpxd7j54282vbs0hj3cm0000gn/T/ipykernel_90868/3241871123.py:7: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  duH_th_spec = (H*np.pi)**-1*math.gamma(1-2*H)*np.cos(H*np.pi)*np.sin(H*np.pi)*math.gamma(2*H+1)*np.array([sigma**2*x**2*(x*2*np.pi)**(1-2*H)/(theta**2+x**2) for x in freqs])\n"
     ]
    }
   ],
   "source": [
    "#Computing the theoretical PSDs of the underlying continuous-time models.\n",
    "white_th_spec = np.array([sigma**2 for x in freqs])\n",
    "u_th_spec = np.array([sigma**2/(theta**2+x**2) for x in freqs])\n",
    "du_th_spec = np.array([sigma**2*x**2/(theta**2+x**2) for x in freqs])\n",
    "fGn_th_spec = (H*np.pi)**-1*math.gamma(1-2*H)*np.cos(H*np.pi)*np.sin(H*np.pi)*math.gamma(2*H+1)*np.array([(x*2*np.pi)**(1-2*H) for x in freqsfGn])\n",
    "uH_th_spec = (H*np.pi)**-1*math.gamma(1-2*H)*np.cos(H*np.pi)*np.sin(H*np.pi)*math.gamma(2*H+1)*np.array([sigma**2*(x*2*np.pi)**(1-2*H)/(theta**2+x**2) for x in freqs])\n",
    "duH_th_spec = (H*np.pi)**-1*math.gamma(1-2*H)*np.cos(H*np.pi)*np.sin(H*np.pi)*math.gamma(2*H+1)*np.array([sigma**2*x**2*(x*2*np.pi)**(1-2*H)/(theta**2+x**2) for x in freqs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(10)\n",
    "if 1:\n",
    "    fBm_sample = np.abs(davies_harte(2*lengthfGn*band_sizefGn,2*lengthfGn*band_sizefGn*OneOverDelta_t,H=H)[:-1])\n",
    "    pd.Series(fBm_sample).to_csv(\"fBm.csv\")\n",
    "else:\n",
    "    fBm_sample = pd.read_csv(\"fBm.csv\",index_col=0).values.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "np.random.seed(1)\n",
    "#Generating the discrete-time samples of each model.\n",
    "unit_gauss = np.random.normal(0, 1, size=2*length*band_size*OneOverDelta_t)\n",
    "u_sample = [0]\n",
    "noise_fac = sigma * math.sqrt(1/(2*theta)*(1-math.exp(-2*theta*Delta_t)))\n",
    "for i in range(2*length*band_size*OneOverDelta_t - 1):\n",
    "    u_sample.append(math.exp(-theta*Delta_t) * u_sample[-1] + noise_fac*unit_gauss[i])\n",
    "u_sample = np.array(u_sample)\n",
    "\n",
    "\n",
    "\n",
    "#Reversing the oversampling by skipping the respective amount of time-steps.\n",
    "dw_sample = sigma * np.random.normal(0, np.sqrt(Delta_t), size=2*length*band_size*OneOverDelta_t)\n",
    "#u_sample = np.array([u_sample[i*oversampling] for i in range(2*length*OneOverDelta_t*band_size)])\n",
    "du_sample = np.diff(u_sample)\n",
    "du_sample = np.append(du_sample,[0])\n",
    "#fBm_sample = dw_sample ###\n",
    "fGn_sample = np.diff(fBm_sample)\n",
    "fGn_sample = np.append(fGn_sample,[0])\n",
    "\n",
    "def fourier(array, type):\n",
    "    if type == \"dt\":\n",
    "        return fft.fft(array)[0:math.ceil(len(array) / 2)]*Delta_t**0.5/len(array)**0.5\n",
    "    elif type == \"dY\":\n",
    "        return fft.fft(array)[0:math.ceil(len(array) / 2)]/(len(array)*Delta_t)**0.5\n",
    "\n",
    "def power_spectrum(array, type):\n",
    "    return abs(fourier(array, type)**2)\n",
    "\n",
    "def band_seperation(array, band_size=band_size):\n",
    "    if band_size > 1:\n",
    "        return np.array([sum(array[i * band_size:(i + 1) * band_size]) / band_size for i in\n",
    "                         range(math.ceil(len(array) / band_size))])\n",
    "    else:\n",
    "        return array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2000000\n"
     ]
    }
   ],
   "source": [
    "print(len(u_sample))\n",
    "#Calculating the sample PSDs.\n",
    "dw_sample_spec = band_seperation(power_spectrum(dw_sample,\"dY\"))\n",
    "u_sample_spec = band_seperation(power_spectrum(u_sample,\"dt\"))\n",
    "du_sample_spec = band_seperation(power_spectrum(du_sample,\"dY\"))\n",
    "fGn_sample_spec = band_seperation(power_spectrum(fGn_sample,\"dY\"),band_sizefGn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 530x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting Figure 1 in the main text with fGn.\n",
    "fig, axs = plt.subplots(2,2,figsize=(5.3,5))\n",
    "\n",
    "samplewidth = 1\n",
    "samplecolor = \"black\"\n",
    "theowidth = 1.5\n",
    "theocolor = \"red\"\n",
    "\n",
    "\n",
    "axs[0,0].set_ylim(10e-4, 200)\n",
    "axs[0,0].set_ylabel(r\"$S_{\\mathrm{d}W}(\\omega)$\")\n",
    "axs[0,0].set_xlabel(r\"$\\omega$\")\n",
    "axs[0,0].text(0.03, 0.08, \"(a)\", transform=axs[0,0].transAxes, verticalalignment='top', bbox=props)\n",
    "axs[0,0].loglog(freqs, dw_sample_spec,color=samplecolor,linewidth=samplewidth)\n",
    "axs[0,0].loglog(freqs, white_th_spec,color=theocolor,linewidth=theowidth)\n",
    "\n",
    "axs[0,1].set_ylabel(r\"$S_{U_t\\mathrm{d}t}(\\omega)$\")\n",
    "axs[0,1].set_xlabel(r\"$\\omega$\")\n",
    "axs[0,1].text(0.03, 0.08, \"(b)\", transform=axs[0,1].transAxes, verticalalignment='top', bbox=props)\n",
    "axs[0,1].loglog(freqs, u_sample_spec,color=samplecolor,linewidth=samplewidth)\n",
    "axs[0,1].loglog(freqs, u_th_spec ,color=theocolor,linewidth=theowidth)\n",
    "\n",
    "axs[1,0].set_ylim(10e-9, 10)\n",
    "axs[1,0].set_ylabel(r\"$S_{\\mathrm{d}U}(\\omega)$\")\n",
    "axs[1,0].set_xlabel(r\"$\\omega$\")\n",
    "axs[1,0].text(0.03, 0.08, \"(c)\", transform=axs[1,0].transAxes, verticalalignment='top', bbox=props)\n",
    "axs[1,0].loglog(freqs, du_sample_spec,color=samplecolor,linewidth=samplewidth)\n",
    "axs[1,0].loglog(freqs, du_th_spec ,color=theocolor,linewidth=theowidth)\n",
    "\n",
    "axs[1,1].set_ylabel(r\"$S_{\\mathrm{d}B^H}(\\omega)$\")\n",
    "axs[1,1].set_xlabel(r\"$\\omega$\")\n",
    "axs[1,1].text(0.03, 0.08, \"(d)\", transform=axs[1,1].transAxes, verticalalignment='top', bbox=props)\n",
    "axs[1,1].loglog(freqsfGn, fGn_sample_spec,color=samplecolor,linewidth=samplewidth)\n",
    "axs[1,1].loglog(freqsfGn, fGn_th_spec ,color=theocolor,linewidth=theowidth)\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.savefig(\"Plots/specs.pdf\",dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysing and plotting the autocovariance functions\n",
    "Increase length to 100000 for this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [],
   "source": [
    "dw_sample2 = dw_sample[::round(OneOverDelta_t*tau)]\n",
    "u_sample2 = u_sample[::round(OneOverDelta_t*tau)]\n",
    "du_sample2 = np.append(np.diff(u_sample2),[0])\n",
    "fBm_sample2 = fBm_sample[::round(OneOverDelta_t*tau)]\n",
    "fGn_sample2 = np.append(np.diff(fBm_sample2),[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Computing the theoretical ACFs of the underlying continuous-time models.\n",
    "white_th_acf = np.array([sigma**2*Delta_t] + [0 for x in lags_th[1:]])\n",
    "u_th_acf = np.array([sigma**2/(2*theta)*np.exp(-theta*x) for x in lags_th])\n",
    "du_th_acf = np.array([sigma**2/(2*theta)*(2*np.exp(-theta*x)-np.exp(-theta*np.abs(tau-x))-np.exp(-theta*np.abs(tau+x))) for x in lags_th])\n",
    "def fBm_cov(t,s):\n",
    "    return 1/2*(t**(2*H)+s**(2*H)-np.abs(t-s)**(2*H))\n",
    "fGn_th_acf = np.array([fBm_cov(tau,tau+x) + fBm_cov(0,x) - fBm_cov(tau,x) - fBm_cov(0,tau+x) for x in lags_th])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculating the sample ACFs.\n",
    "dw_sample_acf = statsmodels.tsa.stattools.acovf(dw_sample2,nlag=nlags-1)\n",
    "u_sample_acf = statsmodels.tsa.stattools.acovf(u_sample2,nlag=nlags-1)\n",
    "du_sample_acf = statsmodels.tsa.stattools.acovf(du_sample2,nlag=nlags-1)\n",
    "fGn_sample_acf = statsmodels.tsa.stattools.acovf(fGn_sample2,nlag=nlags-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 530x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting Figure 2 in the main text with fGn.\n",
    "fig, axs = plt.subplots(2,2,figsize=(5.3,5))\n",
    "\n",
    "samplewidth = 2\n",
    "samplecolor = \"black\"\n",
    "theowidth = 1.5\n",
    "theocolor = \"red\"\n",
    "\n",
    "\n",
    "\n",
    "axs[0,0].set_ylabel(r\"$\\mathrm{ACF}_{\\mathrm{d}W}(\\tau)$\")\n",
    "axs[0,0].set_xlabel(r\"$\\tau$\")\n",
    "axs[0,0].text(0.91, 0.97, \"(a)\", transform=axs[0,0].transAxes, verticalalignment='top', bbox=props)\n",
    "axs[0,0].scatter(lags, dw_sample_acf,color=samplecolor, marker=\"x\")\n",
    "axs[0,0].plot(lags_th, white_th_acf,color=theocolor,linewidth=theowidth)\n",
    "\n",
    "axs[0,1].set_ylabel(r\"$\\mathrm{ACF}_{U\\mathrm{d}t}(\\tau)$\")\n",
    "axs[0,1].set_xlabel(r\"$\\tau$\")\n",
    "axs[0,1].text(0.91, 0.97, \"(b)\", transform=axs[0,1].transAxes, verticalalignment='top', bbox=props)\n",
    "axs[0,1].scatter(lags, u_sample_acf,color=samplecolor, marker=\"x\")\n",
    "axs[0,1].plot(lags_th, u_th_acf,color=theocolor,linewidth=theowidth)\n",
    "\n",
    "#axs[1,0].set_ylim([-0.0001,0.0001])\n",
    "axs[1,0].set_ylabel(r\"$\\mathrm{ACF}_{\\mathrm{d}U}(\\tau)$\")\n",
    "axs[1,0].set_xlabel(r\"$\\tau$\")\n",
    "axs[1,0].text(0.91, 0.97, \"(c)\", transform=axs[1,0].transAxes, verticalalignment='top', bbox=props)\n",
    "axs[1,0].scatter(lags, du_sample_acf,color=samplecolor, marker=\"x\")\n",
    "axs[1,0].plot(lags_th, du_th_acf,color=theocolor,linewidth=theowidth)\n",
    "\n",
    "axs[1,1].set_ylabel(r\"$\\mathrm{ACF}_{\\mathrm{d}B^H}(\\tau)$\", labelpad=0)\n",
    "axs[1,1].ticklabel_format(axis='y', style='sci', scilimits=(0, 0))\n",
    "axs[1,1].set_xlabel(r\"$\\tau$\")\n",
    "axs[1,1].text(0.91, 0.97, \"(d)\", transform=axs[1,1].transAxes, verticalalignment='top', bbox=props)\n",
    "axs[1,1].scatter(lags, fGn_sample_acf,color=samplecolor, marker=\"x\")\n",
    "axs[1,1].plot(lags_th, fGn_th_acf,color=theocolor,linewidth=theowidth)\n",
    "axs[1,1].set_ylim([-0.05,0.35])\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.savefig(\"Plots/acfs.pdf\",dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate a fold bifurcation under Udt and dU noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 10000\n",
    "OneOverDelta_t = 1\n",
    "Delta_t = 1/OneOverDelta_t\n",
    "oversampling = 10\n",
    "tspan = np.linspace(0,T,T*OneOverDelta_t*oversampling, endpoint = False)\n",
    "tspan_plt = np.linspace(0,T,T*OneOverDelta_t, endpoint = False)\n",
    "est_fraction = 0.7\n",
    "stab_fraction = 0.8\n",
    "theta = 1\n",
    "kappa_u = 0.005\n",
    "kappa_du = 0.0032\n",
    "\n",
    "def alpha(t):\n",
    "    #return np.sqrt(12)/9*t/(stab_fraction*T)\n",
    "    #return np.heaviside(1-t/(stab_fraction*T),1)*np.sqrt(12)/9*1/3*(2+t/(stab_fraction*T))+(1-np.heaviside(1-t/(stab_fraction*T),1))*np.sqrt(12)/9\n",
    "    return np.heaviside(1-t/(stab_fraction*T),1)*np.sqrt(12)/9*t/(stab_fraction*T)+(1-np.heaviside(1-t/(stab_fraction*T),1))*np.sqrt(12)/9\n",
    "\n",
    "\n",
    "def f(x,t):\n",
    "    return -x**3+x-alpha(t)\n",
    "\n",
    "def V(x,alpha):\n",
    "    return x**4/4-x**2/2+alpha*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "white_sample = np.random.normal(0, 1, size=T*OneOverDelta_t*oversampling)\n",
    "u_sample = np.zeros(T*OneOverDelta_t*oversampling+1)\n",
    "u_sample[0] = np.random.normal(0, sigma * math.sqrt(1/(2*theta)))\n",
    "noise_fac = sigma * math.sqrt(1/(2*theta)*(1-math.exp(-2*theta*Delta_t/oversampling)))\n",
    "for i in range(T*OneOverDelta_t*oversampling-1):\n",
    "    u_sample[i+1] = math.exp(-theta*Delta_t/oversampling) * u_sample[i] + noise_fac*white_sample[i]\n",
    "\n",
    "du_sample = np.diff(u_sample)\n",
    "u_sample = u_sample[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if 1:\n",
    "    n = T*OneOverDelta_t\n",
    "    upper = np.zeros(n)\n",
    "    lower = np.zeros(n)\n",
    "    unstable = np.zeros(n)\n",
    "\n",
    "    for i in range(n):\n",
    "        sol = scipy.integrate.solve_ivp(lambda t,x: f(x,tspan_plt[i]),(0.0,50),[2.0], method=\"BDF\")\n",
    "        upper[i] = sol.y[0,-1]\n",
    "        sol = scipy.integrate.solve_ivp(lambda t,x: f(x,tspan_plt[i]),(0.0,50),[-2.0], method=\"BDF\")\n",
    "        lower[i] = sol.y[0,-1]\n",
    "        sol = scipy.integrate.solve_ivp(lambda t,x: -f(x,tspan_plt[i]),(0.0,50),[0.0], method=\"BDF\")\n",
    "        unstable[i] = sol.y[0,-1]\n",
    "        \n",
    "    unstable[np.abs(unstable)>1] = np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_u_sample = np.zeros(T*OneOverDelta_t*oversampling)\n",
    "x_u_sample[0] = upper[0]\n",
    "x_du_sample = np.zeros(T*OneOverDelta_t*oversampling)\n",
    "x_du_sample[0] = upper[0]\n",
    "\n",
    "for i in range(T*OneOverDelta_t*oversampling-1):\n",
    "    x_u_sample[i+1] = x_u_sample[i] + f(x_u_sample[i],tspan[i])*Delta_t/oversampling + kappa_u*u_sample[i]*Delta_t/oversampling\n",
    "    x_du_sample[i+1] = x_du_sample[i] + f(x_du_sample[i],tspan[i])*Delta_t/oversampling + kappa_du*du_sample[i]\n",
    "\n",
    "x_u_sample = x_u_sample[::oversampling]\n",
    "x_du_sample = x_du_sample[::oversampling]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "windowsize = 1000\n",
    "skip = 100\n",
    "x_u_var = np.array([np.var(statsmodels.tsa.tsatools.detrend(x_u_sample[i:i+windowsize], order=2)) for i in range(0,T*OneOverDelta_t-windowsize,skip)])\n",
    "x_du_var = np.array([np.var(statsmodels.tsa.tsatools.detrend(x_du_sample[i:i+windowsize], order=2)) for i in range(0,T*OneOverDelta_t-windowsize,skip)])\n",
    "x_u_ac1 = np.array([np.dot(statsmodels.tsa.tsatools.detrend(x_u_sample[i:i+windowsize-1], order=2),statsmodels.tsa.tsatools.detrend(x_u_sample[i+1:i+windowsize], order=2))/np.var(statsmodels.tsa.tsatools.detrend(x_u_sample[i:i+windowsize], order=2))/windowsize for i in range(0,T*OneOverDelta_t-windowsize,skip)])\n",
    "x_du_ac1 = np.array([np.dot(statsmodels.tsa.tsatools.detrend(x_du_sample[i:i+windowsize-1], order=2),statsmodels.tsa.tsatools.detrend(x_du_sample[i+1:i+windowsize], order=2))/np.var(statsmodels.tsa.tsatools.detrend(x_u_sample[i:i+windowsize], order=2))/windowsize for i in range(0,T*OneOverDelta_t-windowsize,skip)])\n",
    "\n",
    "tau_u_var = round(stats.kendalltau(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_u_var[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)])[0],2)\n",
    "tau_du_var = round(stats.kendalltau(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_du_var[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)])[0],2)\n",
    "tau_u_ac1 = round(stats.kendalltau(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_u_ac1[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)])[0],2)\n",
    "tau_du_ac1 = round(stats.kendalltau(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_du_ac1[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)])[0],2)\n",
    "\n",
    "p_u_var = stats.linregress(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_u_var[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)])[0]\n",
    "p_du_var = stats.linregress(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_du_var[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)])[0]\n",
    "p_u_ac1 = stats.linregress(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_u_ac1[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)])[0]\n",
    "p_du_ac1 = stats.linregress(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_du_ac1[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 530x500 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5.3,5))\n",
    "\n",
    "gs = GridSpec(3, 3, figure=fig)\n",
    "pot1plt = fig.add_subplot(gs[0, 0])\n",
    "pot2plt = fig.add_subplot(gs[0, 1], sharey=pot1plt)\n",
    "pot3plt = fig.add_subplot(gs[0, 2], sharey=pot1plt)\n",
    "foldplt = fig.add_subplot(gs[1, :])\n",
    "varplt = fig.add_subplot(gs[2, :], sharex=foldplt)\n",
    "ac1plt = varplt.twinx()\n",
    "\n",
    "staterange = np.linspace(-2,2,50)\n",
    "t1 = 0.02*T\n",
    "t2 = 0.8*T\n",
    "t3 = 0.98*T\n",
    "shortN = 100\n",
    "x_alpha = 0.7\n",
    "\n",
    "pot1plt.plot(staterange,[V(x,alpha(t1)) for x in staterange], c=\"black\")\n",
    "pot1plt.plot(x_u_sample[round(t1*OneOverDelta_t):round(t1*OneOverDelta_t)+shortN],np.linspace(0,2,shortN), c=\"darkred\", alpha = x_alpha)\n",
    "pot1plt.plot(x_du_sample[round(t1*OneOverDelta_t):round(t1*OneOverDelta_t)+shortN],np.linspace(0,2,shortN), c=\"darkblue\", alpha = x_alpha)\n",
    "pot1plt.xaxis.tick_top()\n",
    "pot1plt.set_yticks([])\n",
    "pot1plt.set_ylabel(\"Potential $V(x)$\")\n",
    "pot1plt.text(0.855, 0.15, \"(a)\", transform=pot1plt.transAxes, verticalalignment='top', bbox=props)\n",
    "\n",
    "\n",
    "pot2plt.plot(staterange,[V(x,alpha(t2)) for x in staterange], c=\"black\")\n",
    "pot2plt.plot(x_u_sample[round(t2*OneOverDelta_t):round(t2*OneOverDelta_t)+shortN],np.linspace(0,2,shortN)+0.3, c=\"darkred\", alpha = x_alpha)\n",
    "pot2plt.plot(x_du_sample[round(t2*OneOverDelta_t):round(t2*OneOverDelta_t)+shortN],np.linspace(0,2,shortN)+0.3, c=\"darkblue\", alpha = x_alpha)\n",
    "pot2plt.xaxis.tick_top()\n",
    "pot2plt.set_yticks([])\n",
    "pot2plt.text(0.855, 0.15, \"(b)\", transform=pot2plt.transAxes, verticalalignment='top', bbox=props)\n",
    "\n",
    "pot3plt.plot(staterange,[V(x,alpha(t3)) for x in staterange], c=\"black\")\n",
    "pot3plt.plot(x_u_sample[round(t3*OneOverDelta_t):round(t3*OneOverDelta_t)+shortN],np.linspace(0,2,shortN)-0.4, c=\"darkred\", alpha = x_alpha)\n",
    "pot3plt.plot(x_du_sample[round(t3*OneOverDelta_t):round(t3*OneOverDelta_t)+shortN],np.linspace(0,2,shortN)-0.4, c=\"darkblue\", alpha = x_alpha)\n",
    "pot3plt.xaxis.tick_top()\n",
    "pot3plt.set_yticks([])\n",
    "pot3plt.text(0.855, 0.15, \"(c)\", transform=pot3plt.transAxes, verticalalignment='top', bbox=props)\n",
    "\n",
    "foldplt.plot(x_u_sample, c=\"darkred\", alpha = x_alpha)\n",
    "foldplt.plot(x_du_sample, c=\"darkblue\", alpha = x_alpha)\n",
    "foldplt.plot(tspan_plt[:round(stab_fraction*T*OneOverDelta_t)], upper[:round(stab_fraction*T*OneOverDelta_t)], c=\"black\")\n",
    "foldplt.plot(tspan_plt, unstable, c=\"black\", linestyle=\"dashed\")\n",
    "foldplt.plot(tspan_plt, lower, c=\"black\")\n",
    "foldplt.scatter([t1], [upper[round(t1*OneOverDelta_t)]], facecolors='none', edgecolors=\"black\", marker=\"s\", s=100)\n",
    "foldplt.scatter([t2], [upper[round(t2*OneOverDelta_t)]], facecolors='none', edgecolors=\"black\", marker=\"s\", s=100)\n",
    "foldplt.scatter([t3], [lower[round(t3*OneOverDelta_t)]], facecolors='none', edgecolors=\"black\", marker=\"s\", s=100)\n",
    "foldplt.axvline(est_fraction*T,c=\"black\", linestyle=\"dotted\")\n",
    "plt.setp(foldplt.get_xticklabels(), visible=False)\n",
    "foldplt.set_ylabel(\"$X_t$\")\n",
    "foldplt.text(0.955, 0.95, \"(d)\", transform=foldplt.transAxes, verticalalignment='top', bbox=props)\n",
    "foldplt.set_ylim(-1.4,1.25)\n",
    "\n",
    "varplt.plot(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_u_var[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)], c=\"darkred\", linestyle=\"solid\")\n",
    "varplt.plot(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_du_var[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)], c=\"darkblue\", linestyle=\"solid\")\n",
    "varplt.axvline(est_fraction*T,c=\"black\", linestyle=\"dotted\")\n",
    "#varplt.axhline(kappa_du**2/(2*theta),c=\"darkblue\", linestyle=\"solid\")\n",
    "varplt.set_ylabel(\"Variance\")\n",
    "varplt.set_xlabel(\"Time $t$\")\n",
    "#varplt.legend([tau_u_var, tau_du_var], loc=\"upper right\")\n",
    "#varplt.legend([p_u_var, p_du_var], loc=\"upper right\")\n",
    "ac1plt.plot(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_u_ac1[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)], c=\"darkred\", linestyle=\"dashed\")\n",
    "ac1plt.plot(tspan_plt[windowsize:round(est_fraction*T*OneOverDelta_t):skip], x_du_ac1[:round((est_fraction*T*OneOverDelta_t-windowsize)/skip)], c=\"darkblue\", linestyle=\"dashed\")\n",
    "#ac1plt.axhline(np.exp(-theta),c=\"darkblue\", linestyle=\"dashed\")\n",
    "ac1plt.set_ylabel(\"AC(1)\")\n",
    "#ac1plt.legend([tau_u_ac1, tau_du_ac1], loc=\"lower right\")\n",
    "#ac1plt.legend([p_u_ac1, p_du_ac1], loc=\"lower right\")\n",
    "varplt.text(0.955, 0.95, \"(e)\", transform=varplt.transAxes, verticalalignment='top', bbox=props)\n",
    "\n",
    "plt.savefig(\"Plots/tipping.pdf\",dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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