Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 19.40% per annum.
- PANW price at the close of April 4, 2025 was $153.57 and was lower than the bottom border of the primary price channel by $11.53 (6.99%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 67.56% per annum.
- PANW price at the close of April 4, 2025 was lower than the bottom border of the secondary price channel by $5.04 (3.18%).
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: November 6, 2024
End date: April 3, 2025
a = 6.2701
b = -0.0006
s = 0.0427
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0006) – 1
= -19.40%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0427) – 1
= 18.64%
November 6, 2024 calculations
Top border of price channel:
Exp(Y1,155)
= Exp(a + b × X1,155 + 2 × s)
= Exp(a + b × 1,675 + 2 × s)
= Exp(6.2701 + -0.0006 × 1,675 + 2 × 0.0427)
= Exp(5.3655)
= $213.90
Bottom border of price channel:
Exp(Y1,155)
= Exp(a + b × X1,155 – 2 × s)
= Exp(a + b × 1,675 – 2 × s)
= Exp(6.2701 + -0.0006 × 1,675 – 2 × 0.0427)
= Exp(5.1946)
= $180.30
April 3, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(6.2701 + -0.0006 × 1,823 + 2 × 0.0427)
= Exp(5.2781)
= $195.99
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(6.2701 + -0.0006 × 1,823 – 2 × 0.0427)
= Exp(5.1072)
= $165.20
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 19.40% per annum.
- PANW price at the close of April 4, 2025 was $153.57 and was lower than the bottom border of the primary price channel by $11.53 (6.99%).
Secondary Trend
Start date: February 10, 2025
End date: April 4, 2025
a = 10.7635
b = -0.0031
s = 0.0353
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0031) – 1
= -67.56%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0353) – 1
= 15.17%
February 10, 2025 calculations
Top border of price channel:
Exp(Y1,218)
= Exp(a + b × X1,218 + 2 × s)
= Exp(a + b × 1,771 + 2 × s)
= Exp(10.7635 + -0.0031 × 1,771 + 2 × 0.0353)
= Exp(5.3712)
= $215.13
Bottom border of price channel:
Exp(Y1,218)
= Exp(a + b × X1,218 – 2 × s)
= Exp(a + b × 1,771 – 2 × s)
= Exp(10.7635 + -0.0031 × 1,771 – 2 × 0.0353)
= Exp(5.2300)
= $186.79
April 4, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(10.7635 + -0.0031 × 1,824 + 2 × 0.0353)
= Exp(5.2077)
= $182.68
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(10.7635 + -0.0031 × 1,824 – 2 × 0.0353)
= Exp(5.0665)
= $158.61
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 67.56% per annum.
- PANW price at the close of April 4, 2025 was lower than the bottom border of the secondary price channel by $5.04 (3.18%).
- 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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