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 30.96% per annum.
- CHTR price at the close of July 25, 2025 was $309.75 and was lower than the bottom border of the primary price channel by $44.61 (12.59%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 14.68% per annum.
- CHTR price at the close of July 25, 2025 was lower than the bottom border of the secondary price channel by $33.37 (9.72%). This indicates a possible reversal in the secondary trend direction.
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 CHTR 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: February 5, 2024
End date: July 24, 2025
a = 4.6693
b = 0.0007
s = 0.0734
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 30.96%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0734) – 1
= 34.14%
February 5, 2024 calculations
Top border of price channel:
Exp(Y887)
= Exp(a + b × X887 + 2 × s)
= Exp(a + b × 1,288 + 2 × s)
= Exp(4.6693 + 0.0007 × 1,288 + 2 × 0.0734)
= Exp(5.7679)
= $319.88
Bottom border of price channel:
Exp(Y887)
= Exp(a + b × X887 – 2 × s)
= Exp(a + b × 1,288 – 2 × s)
= Exp(4.6693 + 0.0007 × 1,288 – 2 × 0.0734)
= Exp(5.4742)
= $238.47
July 24, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.6693 + 0.0007 × 1,823 + 2 × 0.0734)
= Exp(6.1633)
= $474.99
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.6693 + 0.0007 × 1,823 – 2 × 0.0734)
= Exp(5.8696)
= $354.10
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 30.96% per annum.
- CHTR price at the close of July 25, 2025 was $309.75 and was lower than the bottom border of the primary price channel by $44.61 (12.59%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: July 26, 2024
End date: July 25, 2025
a = 5.2819
b = 0.0004
s = 0.0642
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 14.68%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0642) – 1
= 29.28%
July 26, 2024 calculations
Top border of price channel:
Exp(Y1,006)
= Exp(a + b × X1,006 + 2 × s)
= Exp(a + b × 1,460 + 2 × s)
= Exp(5.2819 + 0.0004 × 1,460 + 2 × 0.0642)
= Exp(5.9582)
= $386.93
Bottom border of price channel:
Exp(Y1,006)
= Exp(a + b × X1,006 – 2 × s)
= Exp(a + b × 1,460 – 2 × s)
= Exp(5.2819 + 0.0004 × 1,460 – 2 × 0.0642)
= Exp(5.7014)
= $299.30
July 25, 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(5.2819 + 0.0004 × 1,824 + 2 × 0.0642)
= Exp(6.0949)
= $443.57
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.2819 + 0.0004 × 1,824 – 2 × 0.0642)
= Exp(5.8381)
= $343.12
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 14.68% per annum.
- CHTR price at the close of July 25, 2025 was lower than the bottom border of the secondary price channel by $33.37 (9.72%). This indicates a possible reversal in the secondary trend direction.