From 9109be577677e5bb073621867ca8ea7d6a4a8da4 Mon Sep 17 00:00:00 2001 From: Filip Stefaniuk Date: Fri, 6 Sep 2024 07:34:47 -0400 Subject: [PATCH] refactor notebooks and add evaluation for quantile models --- notebooks/btcusdt_dataset.ipynb | 2 +- notebooks/evaluate.ipynb | 167131 ++++++++++++++++++----------- src/ml/data.py | 54 + src/ml/model.py | 13 + src/strategy/strategy.py | 84 +- 5 files changed, 105010 insertions(+), 62274 deletions(-) create mode 100644 src/ml/data.py create mode 100644 src/ml/model.py diff --git a/notebooks/btcusdt_dataset.ipynb b/notebooks/btcusdt_dataset.ipynb index 48626f8..1987161 100644 --- a/notebooks/btcusdt_dataset.ipynb +++ b/notebooks/btcusdt_dataset.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 43, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ diff --git a/notebooks/evaluate.ipynb b/notebooks/evaluate.ipynb index 796d185..370cac2 100644 --- a/notebooks/evaluate.ipynb +++ b/notebooks/evaluate.ipynb @@ -1,5 +1,31 @@ { "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import wandb\n", + "import os\n", + "import pandas as pd\n", + "import plotly.graph_objs as go\n", + "from pytorch_forecasting.models.temporal_fusion_transformer import TemporalFusionTransformer\n", + "from pytorch_forecasting.data.timeseries import TimeSeriesDataSet\n", + "import numpy as np\n", + "import torch\n", + "\n", + "from ml.model import load_model_from_wandb\n", + "from ml.data import get_dataset_from_wandb, get_train_validation_split, build_time_series_dataset" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Evaluate model predicting price (with Quantiles)" + ] + }, { "cell_type": "code", "execution_count": 2, @@ -9,156 +35,52 @@ "name": "stderr", "output_type": "stream", "text": [ - "/usr/local/anaconda3/envs/wnemsc/lib/python3.9/site-packages/pytorch_forecasting/models/base_model.py:30: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", - " from tqdm.autonotebook import tqdm\n" + "Failed to detect the name of this notebook, you can set it manually with the WANDB_NOTEBOOK_NAME environment variable to enable code saving.\n", + "\u001b[34m\u001b[1mwandb\u001b[0m: Downloading large artifact btc-usdt-5m:latest, 310.03MB. 10 files... \n", + "\u001b[34m\u001b[1mwandb\u001b[0m: 10 of 10 files downloaded. \n", + "Done. 0:0:0.4\n", + "/home/filip/anaconda3/envs/wne-msc-thesis/lib/python3.9/site-packages/lightning/pytorch/utilities/parsing.py:208: Attribute 'loss' is an instance of `nn.Module` and is already saved during checkpointing. It is recommended to ignore them using `self.save_hyperparameters(ignore=['loss'])`.\n", + "/home/filip/anaconda3/envs/wne-msc-thesis/lib/python3.9/site-packages/lightning/pytorch/utilities/parsing.py:208: Attribute 'logging_metrics' is an instance of `nn.Module` and is already saved during checkpointing. It is recommended to ignore them using `self.save_hyperparameters(ignore=['logging_metrics'])`.\n" ] } ], "source": [ - "import wandb\n", - "import os\n", - "import pandas as pd\n", - "import plotly.graph_objs as go\n", - "from pytorch_forecasting.models.temporal_fusion_transformer import TemporalFusionTransformer\n", - "from pytorch_forecasting.data.timeseries import TimeSeriesDataSet\n", - "import numpy as np\n", - "import torch" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "def get_dataset_window(run, window=None):\n", - " artifact_name = f\"{run.project}/{run.config['data']['dataset']}\"\n", - " artifact = wandb.Api().artifact(artifact_name)\n", - " base_path = artifact.download()\n", + "RUN_ID = \"filipstefaniuk/wne-masters-thesis-testing/x352wmas\"\n", "\n", - " name = artifact.metadata['name']\n", - " in_sample_name = f\"in-sample-{window or run.config['data']['sliding_window']}\"\n", - " in_sample_data = pd.read_csv(os.path.join(\n", - " base_path, name + '-' + in_sample_name + '.csv'))\n", - " out_of_sample_name = f\"out-of-sample-{window or run.config['data']['sliding_window']}\"\n", - " out_of_sample_data = pd.read_csv(os.path.join(\n", - " base_path, name + '-' + out_of_sample_name + '.csv'))\n", - "\n", - " return in_sample_data, out_of_sample_data\n", - "\n", - "def get_train_validation_split(config, in_sample_data):\n", - " validation_part = config['data']['validation']\n", - " train_data = in_sample_data.iloc[:int(len(in_sample_data) * (1 - validation_part))]\n", - " val_data = in_sample_data.iloc[len(train_data) - config['past_window']:]\n", - "\n", - " return train_data, val_data\n", - "\n", - "def build_time_series_dataset(config, data):\n", - " data = data.copy()\n", - " data['weekday'] = data['weekday'].astype('str')\n", - " data['hour'] = data['hour'].astype('str')\n", - "\n", - " time_series_dataset = TimeSeriesDataSet(\n", - " data,\n", - " time_idx=config['data']['fields']['time_index'],\n", - " target=config['data']['fields']['target'],\n", - " group_ids=config['data']['fields']['group_ids'],\n", - " min_encoder_length=config['past_window'],\n", - " max_encoder_length=config['past_window'],\n", - " min_prediction_length=config['future_window'],\n", - " max_prediction_length=config['future_window'],\n", - " static_reals=config['data']['fields']['static_real'],\n", - " static_categoricals=config['data']['fields']['static_cat'],\n", - " time_varying_known_reals=config['data']['fields']['dynamic_known_real'],\n", - " time_varying_known_categoricals=config['data']['fields']['dynamic_known_cat'],\n", - " time_varying_unknown_reals=config['data']['fields']['dynamic_unknown_real'],\n", - " time_varying_unknown_categoricals=config['data']['fields']['dynamic_unknown_cat'],\n", - " randomize_length=False,\n", - " )\n", - "\n", - " return time_series_dataset" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# TODO: Maybe save all on cpu\n", - "def get_model(run):\n", - " model_name = run.config['model']['name']\n", - " model_path = f\"{run.project}/model-{run.id}:best\"\n", - " model_artifact = wandb.Api().artifact(model_path)\n", - "\n", - " if model_name == 'TemporalFusionTransformer':\n", - " return TemporalFusionTransformer.load_from_checkpoint(model_artifact.file())\n", - "\n", - " raise ValueError(\"Invalid model name\")" + "run = wandb.Api().run(RUN_ID)\n", + "in_sample, out_of_sample = get_dataset_from_wandb(run)\n", + "test_data = out_of_sample\n", + "train_data, valid_data = get_train_validation_split(run.config, in_sample)\n", + "train = build_time_series_dataset(run.config, train_data)\n", + "valid = build_time_series_dataset(run.config, valid_data)\n", + "test = build_time_series_dataset(run.config, test_data)\n", + "model = load_model_from_wandb(run)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, - "outputs": [], - "source": [ - "RUN_ID = \"filipstefaniuk/wne-masters-thesis-testing/r1gtdlsf\"\n", - "PROJECT = \"wne-masters-thesis-testing\"\n", - "run = wandb.Api().run(RUN_ID)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "Failed to detect the name of this notebook, you can set it manually with the WANDB_NOTEBOOK_NAME environment variable to enable code saving.\n", - "\u001b[34m\u001b[1mwandb\u001b[0m: Downloading large artifact btc-usdt-5m:latest, 310.03MB. 10 files... \n", - "\u001b[34m\u001b[1mwandb\u001b[0m: 10 of 10 files downloaded. \n", - "Done. 0:0:0.5\n", - "/usr/local/anaconda3/envs/wnemsc/lib/python3.9/site-packages/lightning/pytorch/utilities/parsing.py:208: Attribute 'loss' is an instance of `nn.Module` and is already saved during checkpointing. It is recommended to ignore them using `self.save_hyperparameters(ignore=['loss'])`.\n", - "/usr/local/anaconda3/envs/wnemsc/lib/python3.9/site-packages/lightning/pytorch/utilities/parsing.py:208: Attribute 'logging_metrics' is an instance of `nn.Module` and is already saved during checkpointing. It is recommended to ignore them using `self.save_hyperparameters(ignore=['logging_metrics'])`.\n" - ] - } - ], - "source": [ - "in_sample, _ = get_dataset_window(run)\n", - "train_data, valid_data = get_train_validation_split(run.config, in_sample)\n", - "train = build_time_series_dataset(run.config, train_data)\n", - "valid = build_time_series_dataset(run.config, valid_data)\n", - "model = get_model(run)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "GPU available: False, used: False\n", + "GPU available: True (cuda), used: True\n", "TPU available: False, using: 0 TPU cores\n", - "HPU available: False, using: 0 HPUs\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/usr/local/anaconda3/envs/wnemsc/lib/python3.9/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:424: The 'predict_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=15` in the `DataLoader` to improve performance.\n" + "HPU available: False, using: 0 HPUs\n", + "LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]\n", + "/home/filip/anaconda3/envs/wne-msc-thesis/lib/python3.9/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:424: PossibleUserWarning:\n", + "\n", + "The 'predict_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=3` in the `DataLoader` to improve performance.\n", + "\n" ] } ], "source": [ "predictions = model.predict(\n", " valid.to_dataloader(train=False, batch_size=64),\n", + " # test.to_dataloader(train=False, batch_size=64),\n", " mode=\"raw\",\n", " return_index=True,\n", " trainer_kwargs={\n", @@ -168,15 +90,15 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Baseline returns 0.23008643692049624\n", - "Strategy returns 0.09137899364187074\n" + "Baseline returns 0.22730028053392815\n", + "Strategy returns 0.15714438080714976\n" ] }, { @@ -190,20765 +112,63336 @@ "type": "scatter", "y": [ 1, - 0.9977269584006767, - 0.997869698623309, - 0.9994982874066667, - 1.0005707679983364, - 0.9993744506189236, - 0.9989117022485251, - 0.9983706396478714, - 0.9986412673942945, - 0.9994386837191079, - 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from strategy.strategy import BuyAndHoldStrategy, PriceQuantilePredictionStrategy\n", + "from strategy.evaluation import evaluate_strategy\n", + "\n", + "model_predictions = pd.DataFrame(predictions.index)\n", + "model_predictions['prediction'] = list(torch.squeeze(predictions.output.prediction).cpu().numpy())\n", + "\n", + "result_baseline = evaluate_strategy(valid_data, BuyAndHoldStrategy())\n", + "result_strategy = evaluate_strategy(valid_data, PriceQuantilePredictionStrategy(model_predictions), exchange_fee=0.001)\n", + "\n", + "print('Baseline returns', result_baseline['total_return'])\n", + "print('Strategy returns', result_strategy['total_return'])\n", + "\n", + "go.Figure([\n", + " go.Scatter(y=result_baseline['portfolio_value']),\n", + " go.Scatter(y=result_strategy['portfolio_value'])]).show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Evaluate model predicting returns (with GMADL loss)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[34m\u001b[1mwandb\u001b[0m: Downloading large artifact btc-usdt-5m:latest, 310.03MB. 10 files... \n", + "\u001b[34m\u001b[1mwandb\u001b[0m: 10 of 10 files downloaded. \n", + "Done. 0:0:0.4\n", + "/home/filip/anaconda3/envs/wne-msc-thesis/lib/python3.9/site-packages/lightning/pytorch/utilities/parsing.py:208: UserWarning:\n", + "\n", + "Attribute 'loss' is an instance of `nn.Module` and is already saved during checkpointing. It is recommended to ignore them using `self.save_hyperparameters(ignore=['loss'])`.\n", + "\n", + "/home/filip/anaconda3/envs/wne-msc-thesis/lib/python3.9/site-packages/lightning/pytorch/utilities/parsing.py:208: UserWarning:\n", + "\n", + "Attribute 'logging_metrics' is an instance of `nn.Module` and is already saved during checkpointing. It is recommended to ignore them using `self.save_hyperparameters(ignore=['logging_metrics'])`.\n", + "\n" + ] + } + ], + "source": [ + "RUN_ID = \"filipstefaniuk/wne-masters-thesis-testing/m6zetdhf\"\n", + "\n", + "run = wandb.Api().run(RUN_ID)\n", + "in_sample, out_of_sample = get_dataset_from_wandb(run)\n", + "train_data, valid_data = get_train_validation_split(run.config, in_sample)\n", + "train = build_time_series_dataset(run.config, train_data)\n", + "valid = build_time_series_dataset(run.config, valid_data)\n", + "test = build_time_series_dataset(run.config, out_of_sample)\n", + "model = load_model_from_wandb(run)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "GPU available: True (cuda), used: True\n", + "TPU available: False, using: 0 TPU cores\n", + "HPU available: False, using: 0 HPUs\n", + "LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]\n", + "/home/filip/anaconda3/envs/wne-msc-thesis/lib/python3.9/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:424: PossibleUserWarning:\n", + "\n", + "The 'predict_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=3` in the `DataLoader` to improve performance.\n", + "\n" + ] + } + ], + "source": [ + "predictions = model.predict(\n", + " valid.to_dataloader(train=False, batch_size=64),\n", + " # test.to_dataloader(train=False, batch_size=64),\n", + " mode=\"raw\",\n", + " return_index=True,\n", + " trainer_kwargs={\n", + " 'logger': False\n", + " })" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Baseline returns 0.2240889082270856\n", + "Strategy returns -0.3902088328046026\n" + ] + }, + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "type": "scatter", + "y": [ + 1, + 1.0009131826823052, + 0.9994057859125508, + 0.9996159730337631, + 0.9990819633796875, + 0.9985869199225123, + 0.9997188591497175, + 1.0001833822851822, + 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" + ] }, "metadata": {}, "output_type": "display_data" @@ -42543,13 +85131,13 @@ ], "source": [ "from strategy.evaluation import evaluate_strategy\n", - "from strategy.strategy import BuyAndHoldStrategy, ModelReturnsPredictionStrategy\n", + "from strategy.strategy import BuyAndHoldStrategy, ReturnsPredictionStrategy\n", "\n", "model_predictions = pd.DataFrame(predictions.index)\n", - "model_predictions['prediction'] = predictions.output.prediction.reshape(-1).numpy()\n", + "model_predictions['prediction'] = predictions.output.prediction.reshape(-1).cpu().numpy()\n", "\n", "result_baseline = evaluate_strategy(valid_data, BuyAndHoldStrategy())\n", - "result_strategy = evaluate_strategy(valid_data, ModelReturnsPredictionStrategy(model_predictions))\n", + "result_strategy = evaluate_strategy(valid_data, ReturnsPredictionStrategy(model_predictions, threshold=0.001))\n", "\n", "print('Baseline returns', result_baseline['total_return'])\n", "print('Strategy returns', result_strategy['total_return'])\n", @@ -42561,7 +85149,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -42574,20742 +85162,20742 @@ { "type": "scatter", "y": [ - -0.000522054557222873, - -0.0005216001300141215, - -0.0003715535858646035, - -0.0004533178289420903, - -0.0005308363470248878, - -0.0005484982393682003, - -0.0004333862161729485, - -0.00038283044705167413, - -0.00035968440352007747, - -0.0003820762212853879, - -0.00036498461849987507, - -0.00037263857666403055, - -0.00038155712536536157, - -0.00033933937083929777, - -0.00016560981748625636, - -0.001146903494372964, - -0.0010510431602597237, - -0.0009021878940984607, - -0.000921485829167068, - -0.0009731689933687449, - -0.0008973696967586875, - -0.0008955963421612978, - -0.0008306183735840023, - -0.0007313373498618603, - -0.0007369829108938575, - -0.0009187567047774792, - -0.0009824639419093728, - 0.0006467014318332076, - 0.0006182193756103516, - 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" + ] }, "metadata": {}, "output_type": "display_data" diff --git a/src/ml/data.py b/src/ml/data.py new file mode 100644 index 0000000..2edabf7 --- /dev/null +++ b/src/ml/data.py @@ -0,0 +1,54 @@ +import os + +import pandas as pd +import wandb +from pytorch_forecasting.data.timeseries import TimeSeriesDataSet + + +def get_dataset_from_wandb(run, window=None): + artifact_name = f"{run.project}/{run.config['data']['dataset']}" + artifact = wandb.Api().artifact(artifact_name) + base_path = artifact.download() + + name = artifact.metadata['name'] + in_sample_name = f"in-sample-{window or run.config['data']['sliding_window']}" + in_sample_data = pd.read_csv(os.path.join( + base_path, name + '-' + in_sample_name + '.csv')) + out_of_sample_name = f"out-of-sample-{window or run.config['data']['sliding_window']}" + out_of_sample_data = pd.read_csv(os.path.join( + base_path, name + '-' + out_of_sample_name + '.csv')) + + return in_sample_data, out_of_sample_data + +def get_train_validation_split(config, in_sample_data): + validation_part = config['data']['validation'] + train_data = in_sample_data.iloc[:int(len(in_sample_data) * (1 - validation_part))] + val_data = in_sample_data.iloc[len(train_data) - config['past_window']:] + + return train_data, val_data + + +def build_time_series_dataset(config, data): + data = data.copy() + data['weekday'] = data['weekday'].astype('str') + data['hour'] = data['hour'].astype('str') + + time_series_dataset = TimeSeriesDataSet( + data, + time_idx=config['data']['fields']['time_index'], + target=config['data']['fields']['target'], + group_ids=config['data']['fields']['group_ids'], + min_encoder_length=config['past_window'], + max_encoder_length=config['past_window'], + min_prediction_length=config['future_window'], + max_prediction_length=config['future_window'], + static_reals=config['data']['fields']['static_real'], + static_categoricals=config['data']['fields']['static_cat'], + time_varying_known_reals=config['data']['fields']['dynamic_known_real'], + time_varying_known_categoricals=config['data']['fields']['dynamic_known_cat'], + time_varying_unknown_reals=config['data']['fields']['dynamic_unknown_real'], + time_varying_unknown_categoricals=config['data']['fields']['dynamic_unknown_cat'], + randomize_length=False, + ) + + return time_series_dataset \ No newline at end of file diff --git a/src/ml/model.py b/src/ml/model.py new file mode 100644 index 0000000..b4a0caa --- /dev/null +++ b/src/ml/model.py @@ -0,0 +1,13 @@ +import wandb +from pytorch_forecasting.models.temporal_fusion_transformer import TemporalFusionTransformer + +# TODO: Maybe save all models on cpu +def load_model_from_wandb(run): + model_name = run.config['model']['name'] + model_path = f"{run.project}/model-{run.id}:best" + model_artifact = wandb.Api().artifact(model_path) + + if model_name == 'TemporalFusionTransformer': + return TemporalFusionTransformer.load_from_checkpoint(model_artifact.file()) + + raise ValueError("Invalid model name") \ No newline at end of file diff --git a/src/strategy/strategy.py b/src/strategy/strategy.py index 215315f..3aa454b 100644 --- a/src/strategy/strategy.py +++ b/src/strategy/strategy.py @@ -34,7 +34,36 @@ class BuyAndHoldStrategy(StrategyBase): dtype=np.int32) -class ModelReturnsPredictionStrategy(StrategyBase): +class ModelPredictionsStrategyBase(StrategyBase): + """Base class for strategies based on model predictions.""" + def __init__(self, + predictions, + name: str = None): + self.predictions = predictions + assert 'time_index' in self.predictions.columns + assert 'group_id' in self.predictions.columns + assert 'prediction' in self.predictions.columns + + self.name = name + + + def info(self): + return {'strategy_name': self.name or 'Unknown model'} + + def run(self, data): + # Adds predictions to data, if prediction is unknown for a given + # item it will be nan. + merged_data = pd.merge( + data, self.predictions, on=['time_index', 'group_id'], + how='left') + + return self.get_positions(merged_data) + + def get_positions(self, data): + raise NotImplementedError() + + +class ReturnsPredictionStrategy(ModelPredictionsStrategyBase): """Strategy that selects position based on returns predictions.""" def __init__( @@ -42,22 +71,11 @@ class ModelReturnsPredictionStrategy(StrategyBase): predictions, threshold=0.001, name=None): - self.predictions = predictions - assert 'time_index' in self.predictions.columns - assert 'group_id' in self.predictions.columns - assert 'prediction' in self.predictions.columns - - self.name = name or "ML Returns prediction" + super().__init__(predictions, name=name) self.threshold = threshold - def info(self) -> Dict[str, Any]: - return {'strategy_name': self.name} - - def run(self, data): - arr = pd.merge( - data, self.predictions, on=['time_index', 'group_id'], - how='left')['prediction'].to_numpy() - + def get_positions(self, data): + arr = data['prediction'] positions = [] for i in range(len(arr)): if arr[i] > self.threshold: @@ -70,3 +88,39 @@ class ModelReturnsPredictionStrategy(StrategyBase): positions.append(positions[-1]) return np.array(positions, dtype=np.int32) + + +class PriceQuantilePredictionStrategy(ModelPredictionsStrategyBase): + def __init__( + self, + predictions, + name=None): + super().__init__(predictions, name=name) + + def info(self): + return {'strategy_name': self.name} + + def get_positions(self, data): + + arr_preds = data['prediction'].to_numpy() + arr_close_price = data['close_price'].to_numpy() + + positions = [] + for i in range(len(arr_preds)): + if not np.isnan(arr_preds[i]).any(): + price = arr_close_price[i] + pred_low = arr_preds[i][0] + pred_high = arr_preds[i][-1] + if (pred_low - price) / price > 0.001: + positions.append(LONG_POSITION) + continue + elif (pred_high - price) / price < -0.001: + positions.append(EXIT_POSITION) + continue + + if not len(positions): + positions.append(EXIT_POSITION) + else: + positions.append(positions[-1]) + + return np.array(positions, dtype=np.int32) \ No newline at end of file