Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 6.14% per annum.
- PANW price at the close of September 16, 2025 was $201.34 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 385.67% per annum.
- PANW price at the close of September 16, 2025 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of PANW price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: August 14, 2024
End date: September 16, 2025
a = 4.9549
b = 0.0002
s = 0.0595
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 6.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0595) – 1
= 26.89%
August 14, 2024 calculations
Top border of price channel:
Exp(Y982)
= Exp(a + b × X982 + 2 × s)
= Exp(a + b × 1,427 + 2 × s)
= Exp(4.9549 + 0.0002 × 1,427 + 2 × 0.0595)
= Exp(5.3071)
= $201.76
Bottom border of price channel:
Exp(Y982)
= Exp(a + b × X982 – 2 × s)
= Exp(a + b × 1,427 – 2 × s)
= Exp(4.9549 + 0.0002 × 1,427 – 2 × 0.0595)
= Exp(5.0689)
= $159.01
September 16, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(4.9549 + 0.0002 × 1,825 + 2 × 0.0595)
= Exp(5.3721)
= $215.31
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.9549 + 0.0002 × 1,825 – 2 × 0.0595)
= Exp(5.1340)
= $169.69
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 6.14% per annum.
- PANW price at the close of September 16, 2025 was $201.34 and was inside the primary price channel.
Secondary Trend
Start date: August 4, 2025
End date: September 16, 2025
a = -2.5880
b = 0.0043
s = 0.0135
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0043) – 1
= 385.67%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0135) – 1
= 5.55%
August 4, 2025 calculations
Top border of price channel:
Exp(Y1,224)
= Exp(a + b × X1,224 + 2 × s)
= Exp(a + b × 1,782 + 2 × s)
= Exp(-2.5880 + 0.0043 × 1,782 + 2 × 0.0135)
= Exp(5.1546)
= $173.23
Bottom border of price channel:
Exp(Y1,224)
= Exp(a + b × X1,224 – 2 × s)
= Exp(a + b × 1,782 – 2 × s)
= Exp(-2.5880 + 0.0043 × 1,782 – 2 × 0.0135)
= Exp(5.1006)
= $164.11
September 16, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(-2.5880 + 0.0043 × 1,825 + 2 × 0.0135)
= Exp(5.3408)
= $208.68
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(-2.5880 + 0.0043 × 1,825 – 2 × 0.0135)
= Exp(5.2867)
= $197.70
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 385.67% per annum.
- PANW price at the close of September 16, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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