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 1,314.53% per annum.
- IBM price at the close of October 26, 2026 was $253.44 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 2,837.44% per annum.
- IBM price at the close of October 26, 2026 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 IBM 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: October 5, 2026
End date: October 26, 2026
a = 2.1135
b = 0.0073
s = 0.0159
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0073) – 1
= 1,314.53%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0159) – 1
= 6.59%
October 5, 2026 calculations
Top border of price channel:
Exp(Y310)
= Exp(a + b × X310 + 2 × s)
= Exp(a + b × 451 + 2 × s)
= Exp(2.1135 + 0.0073 × 451 + 2 × 0.0159)
= Exp(5.4190)
= $225.65
Bottom border of price channel:
Exp(Y310)
= Exp(a + b × X310 – 2 × s)
= Exp(a + b × 451 – 2 × s)
= Exp(2.1135 + 0.0073 × 451 – 2 × 0.0159)
= Exp(5.3552)
= $211.70
October 26, 2026 calculations
Top border of price channel:
Exp(Y325)
= Exp(a + b × X325 + 2 × s)
= Exp(a + b × 472 + 2 × s)
= Exp(2.1135 + 0.0073 × 472 + 2 × 0.0159)
= Exp(5.5714)
= $262.80
Bottom border of price channel:
Exp(Y325)
= Exp(a + b × X325 – 2 × s)
= Exp(a + b × 472 – 2 × s)
= Exp(2.1135 + 0.0073 × 472 – 2 × 0.0159)
= Exp(5.5076)
= $246.56
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 1,314.53% per annum.
- IBM price at the close of October 26, 2026 was $253.44 and was inside the primary price channel.
Secondary Trend
Start date: October 12, 2026
End date: October 26, 2026
a = 1.1806
b = 0.0093
s = 0.0151
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0093) – 1
= 2,837.44%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0151) – 1
= 6.24%
October 12, 2026 calculations
Top border of price channel:
Exp(Y315)
= Exp(a + b × X315 + 2 × s)
= Exp(a + b × 458 + 2 × s)
= Exp(1.1806 + 0.0093 × 458 + 2 × 0.0151)
= Exp(5.4522)
= $233.27
Bottom border of price channel:
Exp(Y315)
= Exp(a + b × X315 – 2 × s)
= Exp(a + b × 458 – 2 × s)
= Exp(1.1806 + 0.0093 × 458 – 2 × 0.0151)
= Exp(5.3917)
= $219.58
October 26, 2026 calculations
Top border of price channel:
Exp(Y325)
= Exp(a + b × X325 + 2 × s)
= Exp(a + b × 472 + 2 × s)
= Exp(1.1806 + 0.0093 × 472 + 2 × 0.0151)
= Exp(5.5819)
= $265.56
Bottom border of price channel:
Exp(Y325)
= Exp(a + b × X325 – 2 × s)
= Exp(a + b × 472 – 2 × s)
= Exp(1.1806 + 0.0093 × 472 – 2 × 0.0151)
= Exp(5.5213)
= $249.97
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 2,837.44% per annum.
- IBM price at the close of October 26, 2026 was inside the secondary price channel.