{"id":29931,"date":"2024-10-28T03:18:44","date_gmt":"2024-10-28T03:18:44","guid":{"rendered":"http:\/\/atmokpo.com\/w\/?p=29931"},"modified":"2024-11-26T06:50:48","modified_gmt":"2024-11-26T06:50:48","slug":"%eb%94%a5%eb%9f%ac%eb%8b%9d-%ed%8c%8c%ec%9d%b4%ed%86%a0%ec%b9%98-%ea%b0%95%ec%a2%8c-ma-%eb%aa%a8%eb%8d%b8","status":"publish","type":"post","link":"https:\/\/atmokpo.com\/w\/29931\/","title":{"rendered":"\ub525\ub7ec\ub2dd \ud30c\uc774\ud1a0\uce58 \uac15\uc88c, MA \ubaa8\ub378"},"content":{"rendered":"

\n \ub525\ub7ec\ub2dd\uacfc \uba38\uc2e0\ub7ec\ub2dd\uc758 \uc138\uacc4\ub294 \ub0a0\ub85c \ubc1c\uc804\ud558\uace0 \uc788\uc73c\uba70, \uc774\ub294 \ub9ce\uc740 \uc5f0\uad6c\uc790\uc640 \uc5d4\uc9c0\ub2c8\uc5b4\ub4e4\uc5d0\uac8c \uc2e4\uc9c8\uc801\uc778 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \ub370 \ub3c4\uc6c0\uc744 \uc8fc\uace0 \uc788\uc2b5\ub2c8\ub2e4. \uc774 \uae00\uc5d0\uc11c\ub294 \ud30c\uc774\ud1a0\uce58(PyTorch) \ud504\ub808\uc784\uc6cc\ud06c\ub97c \uc0ac\uc6a9\ud558\uc5ec MA(Moving Average) \ubaa8\ub378\uc744 \uad6c\ud604\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc54c\uc544\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. MA \ubaa8\ub378\uc740 \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130 \ubd84\uc11d\uc5d0\uc11c \ub370\uc774\ud130\uc758 \ud3c9\uade0\uc744 \uacc4\uc0b0\ud558\uc5ec \uc608\uce21\ud558\ub294 \ud1b5\uacc4\uc801 \ubc29\ubc95\uc73c\ub85c, \uc8fc\ub85c \ub370\uc774\ud130\uac00 \uc2dc\uac04\uc5d0 \ub530\ub77c \uc5b4\ub5a4 \ud328\ud134\uc744 \ubcf4\uc774\ub294\uc9c0\ub97c \uc774\ud574\ud558\ub294 \ub370 \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 MA \ubaa8\ub378\uc758 \uc774\ub860\uc801 \ubc30\uacbd, \ud30c\uc774\uc36c \uc608\uc81c \ucf54\ub4dc \ubc0f \uad6c\ud604 \uc804\ubc18\uc5d0 \uac78\uce5c \uacfc\uc815\uc5d0 \ub300\ud574 \uc0c1\uc138\ud788 \uc124\uba85\ud558\uaca0\uc2b5\ub2c8\ub2e4.\n<\/p>\n

1. MA \ubaa8\ub378\uc5d0 \ub300\ud55c \uc774\ud574<\/h2>\n

\n MA \ubaa8\ub378\uc740 \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\uc5d0\uc11c \uacfc\uac70\uc758 \uc608\uce21 \uc624\ucc28(error)\ub97c \uc0ac\uc6a9\ud558\uc5ec \ud604\uc7ac\uc758 \uac12\uc744 \uc608\uce21\ud558\ub294 \uc811\uadfc \ubc29\uc2dd\uc785\ub2c8\ub2e4. \uc774\ub294 \uc8fc\ub85c ADL(Autoregressive Distributed Lag) \ubaa8\ub378\uacfc \uacb0\ud569\ud558\uc5ec \uc885\ud569\uc801\uc778 \uc608\uce21 \ubaa8\ub378\uc744 \ud615\uc131\ud558\ub294 \ub370 \uc0ac\uc6a9\ub429\ub2c8\ub2e4.\n<\/p>\n

\n MA \\( q \\) \ubaa8\ud615\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \uc218\uc2dd\uc73c\ub85c \uc815\uc758\ub429\ub2c8\ub2e4:\n<\/p>\n

\nY_t = \u03bc + \u03b8_1\u03b5_{t-1} + \u03b8_2\u03b5_{t-2} + ... + \u03b8_q\u03b5_{t-q} + \u03b5_t\n<\/pre>\n
\n    \uc5ec\uae30\uc11c \\( Y_t \\)\ub294 \ud604\uc7ac \uc2dc\uc810\uc758 \uac12, \\( \u03bc \\)\ub294 \ud3c9\uade0, \\( \u03b8 \\)\ub294 MA \ub9e4\uac1c\ubcc0\uc218, \\( \u03b5 \\)\ub294 \ubc31\uc0c9\uc7a1\uc74c(white noise)\uc785\ub2c8\ub2e4. MA \ubaa8\ub378\uc740 \uc21c\uc11c\ub294 \\( q \\)\uc5d0 \ub530\ub77c \uacb0\uc815\ub418\uba70, \uc774\ub294 \uacfc\uac70\uc758 \uc624\ucc28\ub97c \uba87 \uac1c\uae4c\uc9c0 \ubc18\uc601\ud560 \uac83\uc778\uc9c0\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4.\n<\/p>\n
2. \ud30c\uc774\ud1a0\uce58 \uc124\uce58 \ubc29\ubc95<\/h2>\n
\n    \ud30c\uc774\ud1a0\uce58\ub97c \uc0ac\uc6a9\ud558\uae30 \uc704\ud574\uc11c\ub294 \uba3c\uc800 \ud30c\uc774\uc36c\uacfc \ud30c\uc774\ud1a0\uce58 \ub77c\uc774\ube0c\ub7ec\ub9ac\ub97c \uc124\uce58\ud574\uc57c \ud569\ub2c8\ub2e4. \ub2e4\uc74c\uc758 \uba85\ub839\uc5b4\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc124\uce58\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4:\n<\/p>\n
\npip install torch torchvision\n<\/pre>\n
\n    Jupyter Notebook\uc5d0\uc11c\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc124\uce58\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4:\n<\/p>\n
\n!pip install torch torchvision\n<\/pre>\n
3. \ub370\uc774\ud130 \uc900\ube44<\/h2>\n
\n    MA \ubaa8\ub378\uc744 \uad6c\ud604\ud558\uae30 \uc704\ud574\uc11c\ub294 \uc801\uc808\ud55c \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\ub97c \uc900\ube44\ud574\uc57c \ud569\ub2c8\ub2e4. \uc5ec\uae30\uc5d0\uc11c\ub294 \ub09c\uc218\ub97c \uc0dd\uc131\ud558\uc5ec \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130\ub97c \ub9cc\ub4e4\uaca0\uc2b5\ub2c8\ub2e4.\n<\/p>\n
\nimport numpy as np\nimport pandas as pd\nimport matplotlib.pyplot as plt\n\n# Setting a random seed for reproducibility\nnp.random.seed(42)\n\n# Generating a time series data\nn_points = 200\ntime = np.arange(n_points)\ndata = np.sin(0.1 * time) + np.random.normal(0, 0.5, n_points)\n\n# Creating a pandas DataFrame\ndf = pd.DataFrame(data, columns=['value'])\ndf['time'] = time\ndf.set_index('time', inplace=True)\n\n# Plotting the time series data\nplt.figure(figsize=(12, 6))\nplt.plot(df.index, df['value'], label='Time Series Data')\nplt.title('Generated Time Series Data')\nplt.xlabel('Time')\nplt.ylabel('Value')\nplt.legend()\nplt.show()\n<\/pre>\n
4. MA \ubaa8\ub378 \uad6c\ud604<\/h2>\n
\n    MA \ubaa8\ub378\uc744 \uad6c\ud604\ud558\uae30 \uc704\ud574\uc11c\ub294 \ud30c\uc774\ud1a0\uce58\uc758 Tensor\ub97c \ud65c\uc6a9\ud558\uace0, \ubaa8\ub378\uc744 \uc815\uc758\ud55c \ud6c4, \ud559\uc2b5\ud560 \ub370\uc774\ud130\ub85c \ud6c8\ub828\uc2dc\ucf1c\uc57c \ud569\ub2c8\ub2e4. \ub2e4\uc74c\uc740 MA \ubaa8\ub378\uc744 \uad6c\ud604\ud558\ub294 \uacfc\uc815\uc785\ub2c8\ub2e4.\n<\/p>\n
\nimport torch\nimport torch.nn as nn\n\n# Hyperparameters\nq = 2  # Order of MA model\n\nclass MA_Model(nn.Module):\n    def __init__(self, q):\n        super(MA_Model, self).__init__()\n        self.q = q\n        self.weights = nn.Parameter(torch.randn(q))  # MA coefficients\n\n    def forward(self, x):\n        batch_size, seq_length, _ = x.size()\n        output = torch.zeros(batch_size, seq_length)\n\n        for t in range(1, seq_length):\n            for k in range(self.q):\n                if t - k - 1 >= 0:  # Ensuring we don't go out of bounds\n                    output[:, t] += self.weights[k] * x[:, t - k - 1]\n        return output\n\n# Example use\nmodel = MA_Model(q)\nexample_input = torch.Tensor(data.reshape(1, -1, 1))  # Shape: (1, n_points, 1)\noutput = model(example_input)\n<\/pre>\n
5. \uc190\uc2e4 \ud568\uc218\uc640 \ucd5c\uc801\ud654<\/h2>\n
\n    MA \ubaa8\ub378\uc744 \ud559\uc2b5\ud558\uae30 \uc704\ud574\uc11c\ub294 \uc190\uc2e4 \ud568\uc218 \ubc0f \uc635\ud2f0\ub9c8\uc774\uc800\ub97c \uc815\uc758\ud574\uc57c \ud569\ub2c8\ub2e4. \uc5ec\uae30\uc11c\ub294 \ud3c9\uade0 \uc81c\uacf1 \uc624\ucc28(MSE)\ub97c \uc0ac\uc6a9\ud569\ub2c8\ub2e4.\n<\/p>\n
\ncriterion = nn.MSELoss()  # Loss function\noptimizer = torch.optim.Adam(model.parameters(), lr=0.01)  # Optimizer\n\n# Training the model\nn_epochs = 1000\nfor epoch in range(n_epochs):\n    model.train()\n    optimizer.zero_grad()  # Gradient reset\n    output = model(example_input)  # Forward pass\n    loss = criterion(output.squeeze(), example_input.squeeze())  # Compute loss\n    loss.backward()  # Backward pass\n    optimizer.step()  # Update parameters\n\n    if epoch % 100 == 0:  # Print loss every 100 epochs\n        print(f'Epoch {epoch} Loss: {loss.item()}')\n<\/pre>\n
6. \uacb0\uacfc \uc2dc\uac01\ud654<\/h2>\n
\n    \ud6c8\ub828\uc774 \uc644\ub8cc\ub41c \ud6c4, \ubaa8\ub378\uc758 \uc608\uce21 \uacb0\uacfc\ub97c \uc2dc\uac01\ud654\ud558\uc5ec \uacb0\uacfc\ub97c \ud655\uc778\ud558\uaca0\uc2b5\ub2c8\ub2e4.\n<\/p>\n
\n# Visualizing the results\npredictions = output.detach().numpy().squeeze()\n\nplt.figure(figsize=(12, 6))\nplt.plot(df.index, df['value'], label='Actual Data')\nplt.plot(df.index, predictions, label='Predictions', linestyle='--')\nplt.title('MA Model Predictions vs Actual Data')\nplt.xlabel('Time')\nplt.ylabel('Value')\nplt.legend()\nplt.show()\n<\/pre>\n
7. \uacb0\ub860<\/h2>\n
\n    \uc774\ubc88 \uac15\uc88c\uc5d0\uc11c\ub294 \ud30c\uc774\ud1a0\uce58\ub97c \uc0ac\uc6a9\ud558\uc5ec MA \ubaa8\ub378\uc744 \uad6c\ud604\ud558\ub294 \ubc29\ubc95\uc744 \uc54c\uc544\ubcf4\uc558\uc2b5\ub2c8\ub2e4. MA \ubaa8\ub378\uc740 \uc2dc\uacc4\uc5f4 \ub370\uc774\ud130 \ubd84\uc11d\uc5d0 \uc720\uc6a9\ud55c \ub3c4\uad6c\uc774\uba70, \ub370\uc774\ud130\uac00 \uc2dc\uac04\uc5d0 \ub530\ub77c \uc5b4\ub5a4 \uacbd\ud5a5\uc744 \ubcf4\uc774\ub294\uc9c0\ub97c \uc774\ud574\ud558\ub294 \ub370 \ub3c4\uc6c0\uc744 \uc90d\ub2c8\ub2e4. \ub610\ud55c \ud30c\uc774\ud1a0\uce58\uc758 \uac15\ub825\ud55c \uae30\ub2a5\uc744 \ud65c\uc6a9\ud558\uc5ec \uc190\uc27d\uac8c \ubaa8\ub378\uc744 \uad6c\ucd95\ud558\uace0 \ud559\uc2b5\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.\n<\/p>\n
\n    \uba38\uc2e0\ub7ec\ub2dd\uacfc \ub525\ub7ec\ub2dd\uc758 \uc138\uacc4\ub294 \uacc4\uc18d \ubc1c\uc804\ud558\uace0 \uc788\uc73c\uba70, \uc0c8\ub85c\uc6b4 \uae30\uc220\uacfc \uae30\ubc95\ub4e4\uc774 \uc9c0\uc18d\uc801\uc73c\ub85c \ub4f1\uc7a5\ud558\uace0 \uc788\uc2b5\ub2c8\ub2e4. \uc55e\uc73c\ub85c\ub3c4 \ub2e4\uc591\ud55c \ubaa8\ub378\uacfc \uae30\ubc95\ub4e4\uc744 \ub2e4\ub8e8\ub294 \ube14\ub85c\uadf8\ub97c \uc9c0\uc18d\uc801\uc73c\ub85c \uc5c5\ub370\uc774\ud2b8\ud560 \uc608\uc815\uc774\ub2c8 \ub9ce\uc740 \uad00\uc2ec \ubd80\ud0c1\ub4dc\ub9bd\ub2c8\ub2e4.\n<\/p>\n
\ucc38\uace0 \ubb38\ud5cc<\/h2>\n