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Update app.py

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1
- # ============================================================================
2
- # TIME SERIES FORECASTING TUTORIAL: Prophet, ARIMA, and SARIMA
3
- # ============================================================================
4
- #
5
- # WHAT IS TIME SERIES DATA?
6
- # -------------------------
7
- # Time series data is a sequence of measurements taken at regular intervals
8
- # over time. Examples include:
9
- # - Daily temperature readings
10
- # - Hourly stock prices
11
- # - Monthly sales figures
12
- # - Minute-by-minute sensor readings (like in this code!)
13
- #
14
- # The goal of time series forecasting is to predict FUTURE values based on
15
- # PAST patterns in the data.
16
- #
17
- # KEY CONCEPTS IN TIME SERIES:
18
- # ----------------------------
19
- # 1. TREND: The long-term direction of the data (going up, down, or staying flat)
20
- # Example: Global temperatures have an upward trend over decades
21
- #
22
- # 2. SEASONALITY: Patterns that repeat at regular intervals
23
- # Example: Ice cream sales are higher in summer, lower in winter (yearly cycle)
24
- # Example: Electricity usage is higher during day, lower at night (daily cycle)
25
- #
26
- # 3. NOISE: Random fluctuations that don't follow any pattern
27
- # Example: Unexpected spikes or dips due to random events
28
- #
29
- # THE THREE MODELS WE'LL USE:
30
- # ---------------------------
31
- # 1. ARIMA (AutoRegressive Integrated Moving Average)
32
- # - A classic statistical model
33
- # - Good for data with trends but NO seasonality
34
- # - Uses past values and past errors to predict future
35
- #
36
- # 2. SARIMA (Seasonal ARIMA)
37
- # - ARIMA + ability to handle seasonal patterns
38
- # - Good for data with BOTH trends AND seasonality
39
- # - NOTE: Can be SLOW on large datasets! (see PERFORMANCE section below)
40
- #
41
- # 3. Prophet (by Meta/Facebook)
42
- # - A modern, user-friendly model
43
- # - Automatically detects trends and multiple seasonalities
44
- # - Great for business forecasting with daily/weekly/yearly patterns
45
- #
46
- # ============================================================================
47
- # PERFORMANCE CONSIDERATIONS (IMPORTANT!)
48
- # ============================================================================
49
- # SARIMA can be VERY SLOW on large datasets because:
50
- # - It needs to compute seasonal lags (looking back 's' time steps)
51
- # - Computational complexity grows with data size AND seasonal period
52
- # - A dataset of 4500 points with s=60 could take 20-60 minutes!
53
- #
54
- # SOLUTION: DOWNSAMPLING
55
- # ----------------------
56
- # Instead of using every data point, we can use every Nth point.
57
- # Example: Instead of 4500 minute-by-minute readings, use 75 hourly averages
58
- #
59
- # This is like looking at a photo:
60
- # - Full resolution (4500 pixels): Very detailed, slow to process
61
- # - Thumbnail (75 pixels): Less detail, but captures the main patterns quickly
62
- #
63
- # For SARIMA in this code, we downsample to make it run in ~30 seconds
64
- # instead of 20+ minutes, while still capturing the important patterns.
65
- #
66
- # Prophet and ARIMA are faster, so they use the full resolution data.
67
- # ============================================================================
68
-
69
- # ============================================================================
70
- # REQUIRED PACKAGES
71
- # ============================================================================
72
- # Before running this code, install these packages:
73
- # pip install prophet statsmodels pandas numpy matplotlib gradio
74
-
75
  import numpy as np
76
  import pandas as pd
77
  import matplotlib.pyplot as plt
@@ -176,7 +102,7 @@ PROPHET_N_CHANGEPOINTS = 25
176
  # ============================================================================
177
  # DATA GENERATION
178
  # ============================================================================
179
- # We'll create SYNTHETIC (fake but realistic) environmental sensor data
180
  # This simulates what you might see in a space station or submarine!
181
  #
182
  # We generate 4 types of measurements:
@@ -186,40 +112,6 @@ PROPHET_N_CHANGEPOINTS = 25
186
  # 4. PM (Particulate Matter in μg/m³) - tiny particles in the air
187
 
188
  def smooth_noise(n_points, low, high, window=30):
189
- """
190
- Generate smooth random noise.
191
-
192
- WHY SMOOTH NOISE?
193
- -----------------
194
- Pure random noise looks very jagged and unrealistic. Real sensor data
195
- usually has smoother variations. We achieve this by:
196
- 1. Generating random numbers between 'low' and 'high'
197
- 2. Applying a "moving average" to smooth them out
198
-
199
- WHAT IS A MOVING AVERAGE?
200
- -------------------------
201
- Instead of using each random number directly, we replace it with the
202
- average of itself and its neighbors. This removes sharp spikes.
203
-
204
- Example with window=3:
205
- Original: [10, 2, 8, 4, 6]
206
- Smoothed: [6, 6.67, 4.67, 6, 5] (each value = average of 3 neighbors)
207
-
208
- Parameters:
209
- -----------
210
- n_points : int
211
- How many data points to generate
212
- low : float
213
- Minimum value for random numbers
214
- high : float
215
- Maximum value for random numbers
216
- window : int
217
- How many neighbors to average (bigger = smoother)
218
-
219
- Returns:
220
- --------
221
- numpy array of smoothed random values
222
- """
223
  # Generate random numbers from a UNIFORM distribution
224
  # Uniform means every number between low and high is equally likely
225
  raw_noise = np.random.uniform(low, high, n_points)
@@ -233,31 +125,6 @@ def smooth_noise(n_points, low, high, window=30):
233
 
234
 
235
  def generate_mission_data(seed=42, n_points=4500):
236
- """
237
- Generate synthetic environmental sensor data.
238
-
239
- This creates realistic-looking data with:
240
- - A TREND (gradual increase or decrease over time)
241
- - SEASONALITY (repeating daily and weekly patterns)
242
- - NOISE (random small variations)
243
-
244
- Parameters:
245
- -----------
246
- seed : int
247
- Random seed for reproducibility (same seed = same data every time)
248
- n_points : int
249
- How many minutes of data to generate (4500 = ~3 days)
250
-
251
- Returns:
252
- --------
253
- pandas DataFrame with columns:
254
- - ds: datetime timestamp
255
- - Time_min: minute number (0, 1, 2, ...)
256
- - O2_percent: oxygen percentage
257
- - CO2_ppm: carbon dioxide in parts per million
258
- - VOCs_ppb: volatile organic compounds in parts per billion
259
- - Particulates_ugm3: particulate matter in micrograms per cubic meter
260
- """
261
  # Set random seed so we get the same "random" data each time
262
  # This is important for reproducibility in science!
263
  np.random.seed(seed)
@@ -357,33 +224,6 @@ def generate_mission_data(seed=42, n_points=4500):
357
  # ============================================================================
358
 
359
  def downsample_series(series, factor):
360
- """
361
- Reduce the number of data points by averaging every 'factor' points.
362
-
363
- WHY DOWNSAMPLE?
364
- ---------------
365
- Some algorithms (like SARIMA) are very slow on large datasets.
366
- Downsampling reduces the data size while preserving the overall pattern.
367
-
368
- HOW IT WORKS:
369
- -------------
370
- Original (factor=3): [1, 2, 3, 4, 5, 6, 7, 8, 9]
371
- Downsampled: [2, 5, 8] (average of each group of 3)
372
-
373
- This is similar to how video compression works - instead of storing
374
- every frame, store key frames that capture the important information.
375
-
376
- Parameters:
377
- -----------
378
- series : pandas Series or numpy array
379
- The original data
380
- factor : int
381
- How many points to combine into one (e.g., 60 = hourly from minute data)
382
-
383
- Returns:
384
- --------
385
- numpy array of downsampled values
386
- """
387
  arr = np.array(series)
388
  # Calculate how many complete groups we can make
389
  n_groups = len(arr) // factor
@@ -396,36 +236,6 @@ def downsample_series(series, factor):
396
 
397
 
398
  def upsample_predictions(predictions, factor, target_length):
399
- """
400
- Expand predictions back to original resolution using interpolation.
401
-
402
- WHY UPSAMPLE?
403
- -------------
404
- After SARIMA makes predictions on downsampled data, we need to
405
- "stretch" those predictions back to match the original data length
406
- for fair comparison.
407
-
408
- HOW IT WORKS:
409
- -------------
410
- Downsampled predictions: [10, 20, 30] (3 points)
411
- Upsampled (factor=3): [10, 13, 17, 20, 23, 27, 30, ...] (9 points)
412
-
413
- We use LINEAR INTERPOLATION - drawing straight lines between points
414
- and filling in the values along those lines.
415
-
416
- Parameters:
417
- -----------
418
- predictions : numpy array
419
- Predictions from the downsampled model
420
- factor : int
421
- The downsampling factor used
422
- target_length : int
423
- The desired output length (original test set size)
424
-
425
- Returns:
426
- --------
427
- numpy array of upsampled predictions matching target_length
428
- """
429
  # Create x-coordinates for original predictions
430
  x_original = np.arange(len(predictions)) * factor
431
 
@@ -443,42 +253,6 @@ def upsample_predictions(predictions, factor, target_length):
443
  # ============================================================================
444
 
445
  def train_prophet(train_df, test_df):
446
- """
447
- Train a Prophet model and make predictions.
448
-
449
- HOW PROPHET WORKS (Simplified):
450
- -------------------------------
451
- Prophet breaks down the time series into components:
452
-
453
- y(t) = trend(t) + seasonality(t) + holidays(t) + error(t)
454
-
455
- 1. TREND: Prophet fits a piecewise linear trend (like connecting dots
456
- with straight lines, but allowing the slope to change at "changepoints")
457
-
458
- 2. SEASONALITY: Prophet uses Fourier series (fancy sine/cosine waves)
459
- to capture daily, weekly, and yearly patterns
460
-
461
- 3. HOLIDAYS: Prophet can account for special events (we don't use this here)
462
-
463
- 4. ERROR: The random noise that can't be predicted
464
-
465
- Prophet is great because:
466
- - It handles missing data well
467
- - It automatically detects seasonality
468
- - It's robust to outliers
469
- - It's easy to use!
470
-
471
- Parameters:
472
- -----------
473
- train_df : DataFrame
474
- Training data with 'ds' (datetime) and 'y' (value) columns
475
- test_df : DataFrame
476
- Test data with 'ds' column (we'll predict 'y' values)
477
-
478
- Returns:
479
- --------
480
- numpy array of predictions for the test period
481
- """
482
  # Create and configure the Prophet model
483
  model = Prophet(
484
  growth="linear", # Use linear trend (not logistic)
@@ -505,51 +279,6 @@ def train_prophet(train_df, test_df):
505
 
506
 
507
  def train_arima(train_series, test_len):
508
- """
509
- Train an ARIMA model and make predictions.
510
-
511
- HOW ARIMA WORKS (Simplified):
512
- -----------------------------
513
- ARIMA stands for: AutoRegressive Integrated Moving Average
514
-
515
- Let's break it down:
516
-
517
- 1. AR (AutoRegressive): Predict using past values
518
- "Tomorrow's temperature depends on today's temperature"
519
-
520
- Formula: y(t) = c + φ1*y(t-1) + φ2*y(t-2) + ... + error
521
-
522
- Where φ (phi) are learned weights for each past value
523
-
524
- 2. I (Integrated): Differencing to remove trends
525
- Instead of predicting y(t), we predict the CHANGE: y(t) - y(t-1)
526
-
527
- This converts: [100, 102, 105, 109] (trending up)
528
- Into: [2, 3, 4] (the differences - no trend!)
529
-
530
- 3. MA (Moving Average): Predict using past errors
531
- "If I was wrong yesterday, adjust today's prediction"
532
-
533
- Formula: y(t) = c + θ1*e(t-1) + θ2*e(t-2) + ... + error
534
-
535
- Where e is the error (actual - predicted) from past forecasts
536
-
537
- ARIMA combines all three: AR + I + MA
538
-
539
- LIMITATION: Basic ARIMA doesn't handle seasonality well!
540
- (That's why we have SARIMA)
541
-
542
- Parameters:
543
- -----------
544
- train_series : pandas Series
545
- Historical data to train on
546
- test_len : int
547
- How many future points to predict
548
-
549
- Returns:
550
- --------
551
- numpy array of predictions
552
- """
553
  try:
554
  # Create and fit the ARIMA model
555
  model = ARIMA(train_series, order=ARIMA_ORDER)
@@ -569,50 +298,6 @@ def train_arima(train_series, test_len):
569
 
570
 
571
  def train_sarima(train_series, test_len, original_test_len):
572
- """
573
- Train a SARIMA model on DOWNSAMPLED data for speed, then upsample predictions.
574
-
575
- HOW SARIMA WORKS (Simplified):
576
- ------------------------------
577
- SARIMA = Seasonal ARIMA = ARIMA + Seasonal components
578
-
579
- It adds seasonal versions of AR, I, and MA:
580
-
581
- Regular ARIMA(p,d,q) handles: trends and short-term patterns
582
- Seasonal (P,D,Q,s) handles: repeating seasonal patterns
583
-
584
- Example with daily temperature (s=365 for yearly seasonality):
585
- - Regular AR: "Today's temp depends on yesterday's temp"
586
- - Seasonal AR: "Today's temp also depends on this day LAST YEAR"
587
-
588
- The seasonal differencing (D) removes seasonal trends:
589
- Instead of: y(t) - y(t-1) [regular differencing]
590
- We use: y(t) - y(t-s) [seasonal differencing]
591
-
592
- This removes patterns like "summer is always hotter than winter"
593
-
594
- SPEED OPTIMIZATION:
595
- -------------------
596
- SARIMA is slow on large datasets. To speed it up:
597
- 1. We DOWNSAMPLE the training data (e.g., minute → hourly)
598
- 2. Train on the smaller dataset (much faster!)
599
- 3. UPSAMPLE the predictions back to original resolution
600
-
601
- This trades a small amount of accuracy for a HUGE speed improvement.
602
-
603
- Parameters:
604
- -----------
605
- train_series : pandas Series
606
- DOWNSAMPLED historical data to train on
607
- test_len : int
608
- How many DOWNSAMPLED points to predict
609
- original_test_len : int
610
- Original test length (for upsampling predictions)
611
-
612
- Returns:
613
- --------
614
- numpy array of predictions (upsampled to original resolution)
615
- """
616
  try:
617
  # Create and fit the SARIMA model (called SARIMAX in statsmodels)
618
  # The X in SARIMAX stands for "eXogenous variables" (external factors)
@@ -655,28 +340,6 @@ def train_sarima(train_series, test_len, original_test_len):
655
  # ============================================================================
656
 
657
  def run_prediction(seed, model_choice):
658
- """
659
- Main function that orchestrates the entire prediction pipeline.
660
-
661
- Steps:
662
- 1. Generate synthetic data
663
- 2. Split into training and test sets
664
- 3. Train selected model(s)
665
- 4. Make predictions
666
- 5. Calculate accuracy metrics
667
- 6. Create visualizations
668
-
669
- Parameters:
670
- -----------
671
- seed : int
672
- Random seed for data generation
673
- model_choice : str
674
- Which model to use: "Prophet", "ARIMA", "SARIMA", or "All"
675
-
676
- Returns:
677
- --------
678
- tuple: (metrics_dataframe, seed_string, matplotlib_figure)
679
- """
680
  # ========================================================================
681
  # STEP 1: Generate Data
682
  # ========================================================================
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
  import numpy as np
2
  import pandas as pd
3
  import matplotlib.pyplot as plt
 
102
  # ============================================================================
103
  # DATA GENERATION
104
  # ============================================================================
105
+ # We'll create SYNTHETIC environmental sensor data
106
  # This simulates what you might see in a space station or submarine!
107
  #
108
  # We generate 4 types of measurements:
 
112
  # 4. PM (Particulate Matter in μg/m³) - tiny particles in the air
113
 
114
  def smooth_noise(n_points, low, high, window=30):
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
115
  # Generate random numbers from a UNIFORM distribution
116
  # Uniform means every number between low and high is equally likely
117
  raw_noise = np.random.uniform(low, high, n_points)
 
125
 
126
 
127
  def generate_mission_data(seed=42, n_points=4500):
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
128
  # Set random seed so we get the same "random" data each time
129
  # This is important for reproducibility in science!
130
  np.random.seed(seed)
 
224
  # ============================================================================
225
 
226
  def downsample_series(series, factor):
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
227
  arr = np.array(series)
228
  # Calculate how many complete groups we can make
229
  n_groups = len(arr) // factor
 
236
 
237
 
238
  def upsample_predictions(predictions, factor, target_length):
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
239
  # Create x-coordinates for original predictions
240
  x_original = np.arange(len(predictions)) * factor
241
 
 
253
  # ============================================================================
254
 
255
  def train_prophet(train_df, test_df):
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
256
  # Create and configure the Prophet model
257
  model = Prophet(
258
  growth="linear", # Use linear trend (not logistic)
 
279
 
280
 
281
  def train_arima(train_series, test_len):
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
282
  try:
283
  # Create and fit the ARIMA model
284
  model = ARIMA(train_series, order=ARIMA_ORDER)
 
298
 
299
 
300
  def train_sarima(train_series, test_len, original_test_len):
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
301
  try:
302
  # Create and fit the SARIMA model (called SARIMAX in statsmodels)
303
  # The X in SARIMAX stands for "eXogenous variables" (external factors)
 
340
  # ============================================================================
341
 
342
  def run_prediction(seed, model_choice):
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
343
  # ========================================================================
344
  # STEP 1: Generate Data
345
  # ========================================================================