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 10.39% per annum.
- KO price at the close of September 12, 2025 was $67.01 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 38.84% per annum.
- KO price at the close of September 12, 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 KO 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: April 11, 2025
End date: September 12, 2025
a = 4.7763
b = -0.0003
s = 0.0125
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.39%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0125) – 1
= 5.12%
April 11, 2025 calculations
Top border of price channel:
Exp(Y1,150)
= Exp(a + b × X1,150 + 2 × s)
= Exp(a + b × 1,670 + 2 × s)
= Exp(4.7763 + -0.0003 × 1,670 + 2 × 0.0125)
= Exp(4.2995)
= $73.66
Bottom border of price channel:
Exp(Y1,150)
= Exp(a + b × X1,150 – 2 × s)
= Exp(a + b × 1,670 – 2 × s)
= Exp(4.7763 + -0.0003 × 1,670 – 2 × 0.0125)
= Exp(4.2495)
= $70.07
September 12, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.7763 + -0.0003 × 1,824 + 2 × 0.0125)
= Exp(4.2532)
= $70.33
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.7763 + -0.0003 × 1,824 – 2 × 0.0125)
= Exp(4.2032)
= $66.90
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.39% per annum.
- KO price at the close of September 12, 2025 was $67.01 and was inside the primary price channel.
Secondary Trend
Start date: August 7, 2025
End date: September 12, 2025
a = 6.6698
b = -0.0013
s = 0.0074
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -38.84%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0074) – 1
= 3.00%
August 7, 2025 calculations
Top border of price channel:
Exp(Y1,230)
= Exp(a + b × X1,230 + 2 × s)
= Exp(a + b × 1,788 + 2 × s)
= Exp(6.6698 + -0.0013 × 1,788 + 2 × 0.0074)
= Exp(4.2761)
= $71.96
Bottom border of price channel:
Exp(Y1,230)
= Exp(a + b × X1,230 – 2 × s)
= Exp(a + b × 1,788 – 2 × s)
= Exp(6.6698 + -0.0013 × 1,788 – 2 × 0.0074)
= Exp(4.2465)
= $69.86
September 12, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(6.6698 + -0.0013 × 1,824 + 2 × 0.0074)
= Exp(4.2276)
= $68.55
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(6.6698 + -0.0013 × 1,824 – 2 × 0.0074)
= Exp(4.1980)
= $66.55
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 38.84% per annum.
- KO price at the close of September 12, 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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